Imaginary Kählerian Killing spinors I

Skew Killing spinors

In this paper, we study the existence of a skew Killing spinor (see the definition below) on 2 and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.

黎曼流上横截Killing旋量的几何性质

Geometric aspects of transversal Killing spinors on Riemannian flows

研究了自旋黎曼流上的Killing旋量型方程。我们证明了可积性条件和部分分类的情况下，$M$是一个局部黎曼积，一个Sasakian流形或三维的方程的非平凡的解决方案，这些黎曼流$M$。

齐性 3-$(α,δ)$-Sasaki 流形的 $\mathcal{H}$-Killing 旋量与旋量对偶性

$\mathcal{H}$-Killing Spinors and Spinorial Duality for Homogeneous 3-$(α,δ)$-Sasaki Manifolds

本文提出并研究推广 Killing 旋量的 $\mathcal{H}$-Killing 方程，证明其在齐性 3-$(α,δ)$-Sasaki 空间对偶对上的一一对应，并涵盖 7 维 $\text{G}_2$ 几何中的已知特殊旋量。

Skew Killing spinors in four dimensions

This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $ψ$ is a spinor that satisfies the equation $\nabla$X$ψ$ = AX $\times$ $ψ$ with a skew-symmetric endomorphism A. We consider the degenerate case, where the rank of A is at most two everywhere and the non-degenerate case, where the rank of A is four everywhere. We prove that in the degenerate case the manifold is locally isometric to the Riemannian product R x N with N having a skew Killing spinor and we explain under which conditions on the spinor the spec…

携带广义Killing旋量的半黎曼 $\ ext{spin}^c$ 流形以及 admitting 第一类虚广义Killing旋量的黎曼 $\ ext{spin}^c$ 流形的分类

Semi-Riemannian $\text{spin}^c$ manifolds carrying generalized Killing spinors and the classification of Riemannian $\text{spin}^c$ manifolds admitting a type I imaginary generalized Killing spinor

本文分类了携带第一类虚广义Killing旋量的黎曼spin^c流形，通过构造平行旋量，并研究半黎曼情形及修正Dirac流，同时提供第二类实例。

Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin$^c$ spinors

The complex projective space $\mathbb C P^2$ of complex dimension $2$ has a Spin$^c$ structure carrying Kählerian Killing spinors. The restriction of one of these Kählerian Killing spinors to a surface $M^2$ characterizes the isometric immersion of $M^2$ into $\mathbb C P^2$ if the immersion is either Lagrangian or complex.

Killing旋量与超曲面

Killing spinors and hypersurfaces

该研究针对带Einstein度量且含Killing旋量的旋量流形，用类广义Killing旋量方程的PDE刻画非退化超曲面内蕴几何，并证明了满足对应旋量条件的实解析伪黎曼流形的嵌入结论。

广义Killing旋量作为主旋量丛的Lagrangian截面

Generalized Killing spinors as Lagrangian sections of principal spin bundles

本文建立了三维伪黎曼旋量流形上ε-单位广义Killing旋量与其主旋量丛上Lagrangian截面的一一对应关系。

Generalized Killing spinors on Einstein manifolds

We study generalized Killing spinors on compact Einstein manifolds with positive scalar curvature. This problem is related to the existence compact Einstein hypersurfaces in manifolds with parallel spinors, or equivalently, in Riemannian products of flat spaces, Calabi-Yau, hyperkaehler, G_2 and Spin(7) manifolds.

关于具有多个Killing旋量的伪黎曼流形

On pseudo-Riemannian manifolds with many Killing spinors

设$M$是一个维数为$n$，签名为$s$的伪黎曼自旋流形，用$N$表示实旋量丛的秩。我们证明了$M$是局部齐性的，如果它允许多个${3/4}N$独立的Killing旋量具有相同的Killing数，除非$n\equiv 1 \pmod 4$和$s\equiv 3 \pmod 4$。我们还证明了$M$是局部齐次的，如果它允许$k_+$独立的Killing旋量与Killing数$λ$和$k_-$独立的Killing旋量与Killing数$-λ$，使得$k_++k_->{3/2}N$，除非$n\equiv s\equiv 3\pmod 4$。类似地，具有多于一个${3/4}N$独立\emph{conformal} Killing旋量的伪黎曼流形是\emph{conformally}局部齐次的。对于（正或负）定度量，上述结果中的界${3/4}N$和${3/2}N$可以分别放宽为${1/2}N$和$N$.进一步证明了具有多个${3/4}N$平行旋量的伪黎曼自旋流形是平坦的，并且如果度量是确定的，则${1/4}N$平行旋量是足够的.类似地，一个黎曼自旋流形有多于一个${3/8}N$ Killing旋量，且Killing数为$λ\in \bR$，则它有常曲率$4λ^2$。对于洛伦兹度规或负定度规，在有界${1/2}N$中也是如此。最后，我们给出了允许Killing旋量的（不一定完备的）黎曼流形的一…

Stability of Riemannian manifolds with Killing spinors

Riemannian manifolds with non-zero Killing spinors are Einstein manifolds. Klaus Kröncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in \cite{Kro15}. In this paper, we obtain a new proof for this stability result by using a Bochner type formula in \cite{DWW05} and \cite{Wan91}. Moreover, existence of real Killing spinors is closely related to the Sasaki-Einstein structure. A regular Sasaki-Einstein manifold is essentially the total space of a certain principal $S^{1}$-bundle over a Kähler-Einstein manifold. We prove that if the ba…

Lorenztian几何中的虚Killing旋量

Imaginary Killing Spinors in Lorenztian Geometry

本文研究了Lorentz自旋流形的几何结构，它允许虚Killing旋量。讨论了签名$(2,n-2)$中斜伴随算子的锥构造和规范型分类.衍生的几何包括Brinkmann空间、Lorentzian Einstein-Sasaki空间和某些翘曲积结构。锥的可分解完整性的例外情况是可能的。

Sasakian流形与spin-c Killing旋量

Sasakian manifolds and spin-c Killing spinors

利用复旋量形式理论，证明奇数维黎曼流形在纯性条件下允许具有实Killing常数的纯spin-c Killing旋量当且仅当它是α-Sasakian的，推广了Moroianu的结果，无需单连通或完备性假设。

关于Hijazi不等式和旋量Killing方程的推广的几点注记

Some Remarks on the Hijazi Inequality and Generalizations of the Killing Equation for Spinors

推广了Th. Friedrich（1980）和O. Hijazi（1986，1992）. Friedrich/Kim最近构造的Einstein-Dirac方程的特解就是这些不等式的极限情形的例子。这些估计的极限情况的讨论产生两个新的场方程推广的Killing方程以及旋量场的弱Killing方程。最后，我们讨论了2-和3-维的情况下，更详细。

Generalized Killing spinors and Lagrangian graphs

We study generalized Killing spinors on the standard sphere $\mathbb{S}^3$, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold $S^3\times S^3$ and to great circle flows on $\mathbb{S}^3$. Using our methods we generalize a well known result of Gluck and Gu concerning divergence-free geodesic vector fields on the sphere and we show that the space of Lagrangian submanifolds of $S^3\times S^3$ has at least three connected components.

一类由Ricci张量和度量决定的广义Killing旋量

A class of generalised Killing spinors determined by the Ricci tensor and the metric

本文引入仿射Killing旋量（AKS），在调和曲率和局部共形平坦条件下分类允许AKS的黎曼自旋流形，刻画带平行1-形式的流形，并证明三维曲率齐次流形的局部齐次性及Bianchi度量的完整分类。

Instability of some Riemannian manifolds with real Killing spinors

We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces $N_{k, l}={\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly ${\rm G}_2$ except $N_{1,0}$), and Sasaki Einstein circle bundles over certain irreducible Hermitian symmetric spaces. We also prove the instability of most of the simply connected non-symmetric compact homogeneous Einstein spaces of dimensions $5, 6, $ and $7$, including the strict nearly Kähler ones (except ${\rm G}_2/{\rm SU}(3)$).

低维中的复广义spin-c Killing旋子

Complex generalized spin-c Killing spinors in low dimensions

该文分类了低维黎曼流形上带特定复Killing函数的复广义spin-c Killing旋子，证明了相关猜想不成立，补充了反例并明确了三维情形的等价条件。

Weyl几何中的旋量方程

Spinor equations in Weyl geometry

本文研究了具有CSpin结构的Weyl流形上的Dirac方程、扭量方程和Killing方程。给出了一个共形的Schr“odinger-Lichnerowicz公式，并利用它给出了这些方程的可积性条件。通过引入任意权旋量的Killing方程，将AndreiMoroianu在[9]中的结果推广到如下意义.唯一的非封闭Weyl流形的维数大于大于3，承认解决方案的真正Killing方程是4维和非紧。任何在这些维中存在一个真正的Killing旋量的外尔流形都必须是爱因斯坦-外尔流形。

5维广义Killing旋量

Generalized Killing spinors in dimension 5

本文研究了实维6的Calabi-Yau流形中超曲面的内禀几何，更一般地，研究了由广义Killing旋量定义的5维流形上的SU（2）-结构。我们证明了在实解析情形下，这样的5-流形可以作为超曲面以自然的方式等距嵌入到Calabi-Yau流形中。我们分类的nilmanifold携带这种类型的不变结构，并提出与holonomy SU（3）的相关度量的例子。

Cones of G manifolds and Killing spinors with skew torsion

This paper is devoted to the systematic investigation of the cone construction for Riemannian $G$ manifolds M, endowed with an invariant metric connection with skew torsion $\nabla^c$, a `characteristic connection'. We show how to define a $\bar G$ structure on the cone $\bar M=M\x \R^+$ with a cone metric, and we prove that a Killing spinor with torsion on $M$ induces a spinor on $\bar M$ that is parallel w.\,r.\,t. the characteristic connection of the $\bar G$ structure. We establish the explicit correspondence between classes of metric almost contact structures on $M$ and almost hermitian c…

杂化Killing旋量方程的解与特殊几何

Solution of heterotic Killing spinor equations and special geometry

本文概述了杂化超引力的Killing旋量方程的解。此外，我们描述了所有半超对称解的分类。

单模李群上的有害结构与 Killing 旋子

Harmful structures and Killing spinors on unimodular Lie groups

本文研究单模李群上的有害结构与 Killing 旋子，刻画其左不变有害结构，分类低维伪黎曼李群上的此类结构，相关李群对应特定爱因斯坦度量的主轨道。

Kenmotsu流形与spin-c Killing旋量

Kenmotsu manifolds and spin-c Killing spinors

该研究拓展了第一作者的结果，证明奇数维黎曼流形存在特定spin-c Killing旋量等价于其为精确$\mu$-Kenmotsu流形，还通过两种理论结合给出刻画证明并描述了该流形的整体结构。

伪黎曼可解流形上的爱因斯坦度量和Killing旋量

Einstein metrics and Killing spinors on pseudo-Riemannian solvmanifolds

本文通过nilsoliton构造了一类任意维数和符号的伪Iwasawa可解流形，证明了所有允许Killing旋量的伪Iwasawa可解流形都属于该族，并指出当度量爱因斯坦时唯一可能是双曲半空间。

A holographic principle for the existence of imaginary Killing spinors

Suppose that $Σ=\partialΩ$ is the $n$-dimensional boundary, with positive (inward) mean curvature $H$, of a connected compact $(n+1)$-dimensional Riemannian spin manifold $(Ω^{n+1},g)$ whose scalar curvature $R\ge -n(n+1)k^2$, for some $k\textgreater{}0$. If $Σ$ admits an isometric and isospin immersion $F$ into the hyperbolic space ${\mathbb{H}^{n+1}\_{-k^2}}$, we define a quasi-local mass and prove its positivity as well as the associated rigidity statement. The proof is based on a holographic principle for the existence of an imaginary Killing spinor. For $n=2$, we also show that its limit,…

Totally umbilical hypersurfaces of Spin$^c$ manifolds carrying special spinor fields

Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin$^c$ manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin$^c$ case the result of O. Kowalski stating that, every totally umbilical hypersurface of an Einstein manifold of dimension greater or equal to $3$ is of constant mean curvature. As an application, we prove that there are no extrinsic hypersheres in complete Riemannian Spin manifolds of non-constant sectional curvature carrying a parallel, Killing or imaginary Killing spinor.

关于广义虚的Spin^c-杀虫旋量

On generalized imaginary $\mathrm{Spin}^c$-Killing spinors

研究广义虚Spin^c-杀虫旋量的几何性质，证明当Dirac电流消失时，流形局部等距于实双曲空间，且在特定条件下给出全局几何描述。

三维李群上的广义Killing旋量

Generalised Killing Spinors on Three-Dimensional Lie Groups

本文完整分类了三维李群上的不变广义Killing旋量，证明非平凡解的存在可推出所有不变旋量均为同一自同态下的广义Killing旋量，且分类与左不变度量无关，并首次构造出对任意n>4具有n个不同特征值的齐性流形例子。

洛伦兹几何中的共形Killing旋量和特殊几何结构

Conformal Killing spinors and special geometric structures in Lorentzian geometry - a survey

本文是一个调查的特殊几何结构，承认共形Killing旋量的基础上的讲座，给出了在“特殊几何结构弦论研讨会”，波恩，2001年9月和在ESI，维也纳，2001年11月。我们讨论的情况下，洛伦兹签名和解释的几何形状发生到6维。

Symplectic Killing spinors

Let $(M,ω)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla.$ Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main topic of this paper. We derive a necessary condition satisfied by a symplectic Killing spinor field. The advantage of this condition consists in the fact that it is expressed by a zeroth order operator. This condition helps us substantiona…

三维流形上的高自旋杀戮旋量

Higher spin Killing spinors on 3-dimensional manifolds

研究三维流形上的高自旋杀戮旋量，证明其刚性结果，并明确表达三维球面和三维双曲空间上的高自旋杀戮旋量，探讨积分自旋丛上的杀戮旋量类型方程。

带挠率的Killing旋量与扭量旋量

Killing and twistor spinors with torsion

研究带挠率的黎曼自旋流形上带挠率扭量旋量，将其方程转化为特定联络下的平行条件，证明其零点孤立，给出带挠率Killing旋量与黎曼Killing旋量的对应，构造非平凡实例并给出立方Dirac算子平方的特征值估计应用。

Extended superalgebras from twistor and Killing spinors

The basic first-order differential operators of spin geometry that are Dirac operator and twistor operator are considered. Special types of spinors defined from these operators such as twistor spinors and Killing spinors are discussed. Symmetry operators of massless and massive Dirac equations are introduced and relevant symmetry operators of twistor spinors and Killing spinors are constructed from Killing-Yano (KY) and conformal Killing-Yano (CKY) forms in constant curvature and Einstein manifolds. The squaring map of spinors gives KY and CKY forms for Killing and twistor spinors respectively…

Einstein-Dirac方程的一个局部存在定理

A Local Existence Theorem for the Einstein-Dirac Equation

研究了具有余维单叶理的黎曼自旋流形上的Einstein-Dirac方程和弱Killing方程。我们证明了，对于任何流形$M^n$承认真正的Killing旋量（分别）。平行旋量），则在$M^n \times {\mathbb R}$上存在翘曲乘积度量$\barη$，使得$(M^n \times {\mathbb R}, \barη)$承认Einstein旋量（相应地，弱Killing旋量）。为了证明这一结果，我们利用Cartan标架理论将Einstein-Dirac方程分解为发展方程和约束，并利用约束的局部保持性质.

曲面到三维齐次流形的旋量特征

Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds

利用一个特殊的旋量（称为广义Killing旋量）的存在性，给出了等距浸入曲面到具有四维等距群的三维齐次流形中的旋量刻画.这推广了T. Friedrich为$\R^3$和B. Morel用于$\Ss^3$和$\HH^3$。本文的主要论点是将广义Killing旋量的能量动量张量解释为依赖于周围空间结构的张量的第二基本形式

关于横向杀戮的刺手的评论

Remarques sur les spineurs de Killing transversaux

本文给出了在具有黎曼流的自旋流形上横截Killing旋量存在的必要条件。

Killing spinor-valued forms and their integrability conditions

We study invariant systems of PDEs defining Killing vector-valued forms, and then we specialize to Killing spinor-valued forms. We give a detailed treatment of their prolongation and integrability conditions by relating the point-wise values of solutions to the curvature of the underlying manifold. As an example, we completely solve the equations on model spaces of constant curvature producing brand new solutions which do not come from the tensor product of Killing spinors and Killing-Yano forms.

超引力中四通量的Killing旋量

Killing spinors in supergravity with 4-fluxes

研究了含挠3-形式$\T$和通量4-形式$\F$的超引力旋量Killing方程.在7维空间中，我们构造了3-Sasakian几何、近平行$\G_2$几何和齐次Aloff-Wallach空间上的紧致解的显式族。约束$\F \cdot Ψ= 0$定义解的非空子族。我们调查的约束$\T \cdot Ψ= 0$，太，并表明，它挑出一个非常特殊的选择的数值参数的Killing方程，这也可以证明几何。

D=11 Killing旋量的几何

The Geometry of D=11 Killing Spinors

我们提出了一种方法来分类所有的超对称配置的D=11超引力使用的G-结构定义的Killing旋量。我们证明，最一般的玻色子几何允许一个Killing旋量至少有一个局部SU（5）或（Spin（7）\ltimes R^8）× R结构，这取决于Killing旋量构造的Killing矢量是类时的还是零的。在前一种情况下，我们确定了存在哪种局部SU（5）结构，并表明几乎所有的几何形式都由结构决定。我们还推导出为了满足运动方程还必须附加什么条件。我们说明的形式主义与一些已知的解决方案，并提出了一些新的解决方案，包括旋转概括的解决膜解决方案和概括最近构建的D=11哥德尔解决方案。

Killing spinor-valued forms and the cone construction

On a pseudo-Riemannian manifold $\mathcal{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $\mathcal{M}$ and parallel fields on the metric cone over $\mathcal{M}$ for spinor-valued forms.

四元数Killing旋量

Quaternionic Killing Spinors

在前一篇文章中，我们证明了四元数Kaehler流形上Dirac算子谱的一个下界。在本文中，我们研究的极限情况下，即。e.流形，其中下界作为特征值获得。我们给出了一个等价的四元数Killing方程，并证明了唯一具有最小可能特征值的对称四元数Kaehler流形是四元数射影空间。

黎曼自旋流形上的Einstein-Dirac方程

The Einstein-Dirac Equation on Riemannian Spin Manifolds

我们构造了Einstein-Dirac方程的精确解，该方程通过能量动量张量将引力场与Dirac算子的本征旋量耦合起来。为此，我们引入一个新的场方程推广的概念杀死旋。这个旋量场方程的解称为弱Killing旋量（WK-旋量）。它们是Einstein-Dirac方程的特解，在n=3维中两个方程基本重合。证明了任何具有以某种特殊方式与度量张量以及切触结构相关的Ricci张量的Sasakian流形都存在WK-旋量。这一结果是一个后果的调查特殊旋量场方程的Sasakian流形（Sasakian准Killing旋量）。总之，在奇数维中，接触几何产生爱因斯坦-狄拉克方程的解。此外，我们还证明了在n > 8的所有维数下，Einstein-Dirac方程的解的存在性，这些解不是WK-旋量。

Kählerian Killing旋量、复接触结构和扭量空间

Kählerian Killing Spinors, Complex Contact Structures and Twistor Spaces

我们收集了我们最近的结果（[5]和[8]），并在一定条件下得到了标题中三个概念的等价性。然后，我们使用这个等价性，以证明有关Sasakian流形，复几乎接触结构和复k-接触结构的一些后果。

The spinorial energy functional: solutions of the gradient flow on Berger spheres

We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Weiß, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, for special cases, we prove that the volume-normalized standard 3-sphere together with a Killing spinor is a stable critical point of the volume-normalized version of the flow. Our results also include an example of a critical point of the volume-normalized flow on the 3-sphere, which is not a Killing spinor.

Killing旋量是黎曼超几何中的Killing向量场

Killing spinors are Killing vector fields in Riemannian Supergeometry

超流形M与任意伪黎曼自旋流形（M_0，g_0）正则相关.将度量g_0推广到T_p M，p \in M_0上的双线性型g（p）的域g，（M，g）的伪黎曼超几何被表示为M上的G-结构，其中G是具有偶部分G_0 \cong Spin（k，l）的超群，（k，l）是（M_0，g_0）的签名.根据定义，（M，g）上的Killing向量场是这个G-结构的无穷小自同构。对于每个旋量场s，M上存在一个相应的奇向量场X_s。我们的主要结果是：X_s是（M，g）上的Killing向量场当且仅当s是扭量旋量。特别地，任何Killing旋量s定义一个Killing向量场X_s。

虚 Killing 施瓦茨尔的因果特性及旋量切片

Causal character of imaginary Killing spinors and spinorial slicings

研究通过虚 Killing 施瓦茨尔的因果特性，探讨高维引力波和黑洞的 BPS 界限，并构造二维余维切片。

7维Killing旋量方程与可积G_2流形的几何

Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds

我们计算了7维${G}_2$ -流形的数量曲率，其中流形允许一个具有全反对称挠率的联系。本文证明了Killing旋量方程的通解公式，并用伸缩函数和NS 3型场表示了解的黎曼数量曲率.在n=7维中，第二费米子弦方程中的膨胀函数可以解释为基本的可积${G}_2$ -结构共形变化为纯$W_3$型的共形变化。

The exact solutions to an Einstein-Dirac-Maxwell system with Sasakian quasi-Killing spinors on 4D spacetimes

Exact solutions to an Einstein-Maxwell(E-D-M) system with an electric current are simple models of global cosmic magnetic phenomena in the universe. In this paper, we consider an E-D-M system with two chiral spinors $ ψ^\pm$ coupled with a gauge field $ A$ and an electromagnetic field $F=dA$. We construct a family of exact solutions to the E-D-M system on four-dimensional static Sasakian spacetimes. The electromagnetic field in the solutions is a contact magnetic field, and the chiral spinors are induced from Sasakian quasi-Killing spinors. We find closed universe models whose weak energy cond…

Computation of generalized Killing spinors on reductive homogeneous spaces

We determine the holonomy of generalized Killing spinor covariant derivatives of the form $D= \nabla + Ω$ on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where $Ω: TM \rightarrow Λ^*(TM)$ is a left-invariant homomorphism. This is essentially an application of the theory of invariant principal bundle connections defined over homogeneous principal bundles. Moreover, the algorithm allows a computation of the associated Killing superalgebra in certain cases. The procedure is demonstrated by determining the supersymmetries of certain homogeneous M2 duals…

The twistor spinors of generic 2- and 3-distributions

Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition. Moreover, we show that given such a twistor spinor we can decompose a conformal Killing field of the structure. We obtain explicit formulas relating conf…

Ricci flow, Killing spinors, and T-duality in generalized geometry

We introduce a notion of Ricci flow in generalized geometry, extending a previous definition by Gualtieri on exact Courant algebroids. Special stationary points of the flow are given by solutions to first-order differential equations, the Killing spinor equations, which encompass special holonomy metrics with solutions of the Hull-Strominger system. Our main result investigates a method to produce new solutions of the Ricci flow and the Killing spinor equations. For this, we consider T-duality between possibly topologically distinct torus bundles endowed with Courant structures, and demonstrat…

四维流形中超曲面通过旋量的等距浸入

Isometric Immersions of Hypersurfaces in 4-dimensional Manifolds via Spinors

本文利用特殊旋量场的存在性，给出了四维空间型和积空间$\M^3(κ)\times\R$中等距浸入超曲面的旋量特征，称之为广义Killing旋量或Dirac方程的等价解.这推广到更高的维度，最近的几个结果的表面T。弗里德里希湾莫瑞尔和两位作者。主要的论点是解释的能量动量张量的广义Killing旋量作为第二基本型，可能高达张量取决于周围的空间。作为应用，我们给出了四维欧几里得空间中超曲面的一个不存在性结果。

(M-theory-)Killing spinors on symmetric spaces

We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form $D= \nabla + Ω$ in a purely algebraic and algorithmic way, where $Ω: TM \rightarrow Λ^*(TM)$ is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e. $(M,g,F)$ with $(M,g)$ a symmetric space and $F$ an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric s…