Junwen Chen, Xiao Zhang
We construct two types of Eguchi-Hanson metrics with the negative constant scalar curvature. The type I metrics are Kähler. The type II metrics are ALH whose total energy can be negative.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
The Dirac equation on metrics of Eguchi-Hanson type
本文研究Eguchi-Hanson型度量上的Dirac方程，证明复平行旋量空间为复二维，并对零标量曲率情形显式求解调和旋量。
Geodesics on metrics of Eguchi-Hanson type
本文研究Eguchi-Hanson型标量平坦及Ricci平坦度量上的测地线方程，给出若干角度或r为常数时的可解情形，并指出仅ψ为常数时显式解尚待解决。
Let $g_{EH}$ be the Eguchi-Hanson metric on the blow-up of $\mathbb{C}^2$ at the origin. In this paper we show that $mg_{EH}$ is not balanced for any positive integer $m$.
In this work we illustrate some well-known facts about the evolution of $S^3$ under the Ricci flow. The Dirac flow we introduce allows us to describe the 4- dimensional metrics with constant curvature. Another new flow leads to the Eguchi-Hanson metric and can be defined either on metric or on corresponding contact forms.
We show that a Ricci flow in four dimensions can develop singularities modeled on the Eguchi-Hanson space. In particular, we prove that starting from a class of asymptotically cylindrical $U(2)$-invariant initial metrics on $TS^2$, a Type II singularity modeled on the Eguchi-Hanson space develops in finite time. Furthermore, we show that for these Ricci flows the only possible blow-up limits are (i) the Eguchi-Hanson space, (ii) the flat $\mathbb{R}^4 /\mathbb{Z}_2$ orbifold, (iii) the 4d Bryant soliton quotiented by $\mathbb{Z}_2$, and (iv) the shrinking cylinder $\mathbb{R} \times \mathbb{R}…
Eguchi--Hanson metrics arising from Kahler--Einstein edge metrics
本文在Calabi–Hirzebruch流形上构造沿两个除子奇异的Kähler–Einstein边缘度量，研究锥角取极值时的Gromov–Hausdorff极限，证明Eguchi–Hanson度量自然出现，并完整描述所有极限行为，解决了Cheltsov–Rubinstein猜想。
A detailed look at the Calabi-Eguchi-Hanson spaces
本文详细研究了复射影空间标准线丛上的Calabi-Eguchi-Hanson Ricci平坦度量，将其刻画为orbifold奇点的解消，并通过显式计算曲率证明了所有紧致极小子流形均位于零截面中，推广了Tsai和Wang的结果。
In 1978, Gibbons-Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with $16$ orbifold points, and resolves the orbifold singularities by gluing in $16$ small Eguchi-Hanson manifolds which all have the same orientation. This construction was carried out rigorously by Topiwala, LeBrun-Singer, and Donaldson. In 1981, Page asked whether the above construction can be modified by reversing the orientations of some of the Eguchi-Hanson manifolds. This is a subtle question: if…
An analytical characterization of Eguchi-Hanson space and its higher-dimensional analogs
研究通过分析ALE流形的Lichnerowicz拉普拉斯算子的L²核维度，证明其为Eguchi-Hanson空间或平坦的Z₂ orbifold，同时推广到高维Kähler ALE orbifold的唯一性结果。
We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol [0,2,1_2]. We construct approximations for the eigenfunctions and their asymptotic scattering phases with the help of the Liouville-Green approximation (WKB). Furthermore, for specific discrete eigenvalues obtained by a continued T-fraction we construct the solution by the Frobenius method and determine its scattering phase by a monodromy computation.
We verify the extension to the zero section of momentum construction of Kaehler-Einstein metrics and Kaehler-Ricci solitons on the total space Y of positive rational powers of the canonical line bundle of toric Fano manifolds with possibly irregular Sasaki-Einstein metrics. More precisely, we show that the extended metric along the zero section has an expression which can be extended to Y, restricts to the associated unit circle bundle as a transversely Kaehler-Einstein (Sasakian eta-Einstein) metric scaled in the Reeb flow direction, and that there is a Riemannian submersion from the scaled S…
We give a new construction of compact Riemannian 7-manifolds with holonomy $G_2$. Let $M$ be a torsion-free $G_2$-manifold (which can have holonomy a proper subgroup of $G_2$) such that $M$ admits an involution $ι$ preserving the $G_2$-structure. Then $M/{\langle ι\rangle}$ is a $G_2$-orbifold, with singular set $L$ an associative submanifold of $M$, where the singularities are locally of the form $\mathbb R^3 \times (\mathbb R^4 / \{\pm 1\})$. We resolve this orbifold by gluing in a family of Eguchi-Hanson spaces, parametrized by a nonvanishing closed and coclosed $1$-form $λ$ on $L$. Much of…
We study the geometry of families of hypersurfaces in Eguchi-Hanson space that arise as complex line bundles over curves in $S^2$ and are three-dimensional, non-compact Riemannian manifolds, which are foliated in Hopf tori for closed curves. They are negatively curved, asymptotically flat spaces, and we compute the complete three-dimensional curvature tensor as well as the second fundamental form, giving also some results concerning their geodesic flow. We show the non-existence of $Ł^p$-harmonic functions on these hypersurfaces for every $p \geq 1$ and arbitrary curves, and determine the infi…
Eguchi-Hanson harmonic spinors revisited
本文重新探讨了 Eguchi-Hanson 空间上的 Dirac 算子零模问题，利用 spin-$c$ 旋量形式体系简化了计算，无需计算旋量联络即可重现扭曲 Dirac 算子的可归一化零模，并将结果推广至更广泛的 Ricci-flat Kähler 流形。
We construct infinitely many new 1-parameter families of simply connected complete noncompact G_2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the nature of the asymptotic geometry changes at two special parameter values: at one special value we obtain a unique member of each family with asymptotically conical (AC) geometry; on approach to the other special parameter value the family of metrics collapses to an AC Calabi-Yau 3-fold. Our infinitely many new diffeomorphism types of AC G_2-ma…
We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds admits a metric projective compactification. We construct a para--$c$--projective compactification of neutral signature Einstein metrics canonically defined on certain rank--$n$ affine bundles $M$ over $n$-dimensional manifolds endowed with projective structures.
A hyperKähler potential is a function rho that is a Kähler potential for each complex structure compatible with the hyperKähler structure. Nilpotent orbits in a complex simple Lie algebra are known to carry hyperKähler metrics admitting such potentials. In this paper, we explicitly calculate the hyperKähler potential when the orbit is of cohomogeneity two. In some cases, we find that this structure lies in a one-parameter family of hyperKähler metrics with Kähler potentials, generalising the Eguchi-Hanson metrics in dimension four.
The generalized Feix--Kaledin construction shows that c-projective $2n$-manifolds with curvature of type $(1,1)$ are precisely the submanifolds of quaternionic $4n$-manifolds which are fixed points set of a special type of quaternionic $S^1$ action $v$. In this paper, we consider this construction in the presence of infinitesimal symmetries of the two geometries. First, we prove that the submaximally symmetric c-projective model with type $(1,1)$ curvature is a submanifold of a submaximally symmetric quaternionic model, and show how this fits into the construction. We give conditions for when …
Hyperkaehler Marriage of the two sphere with the hyperbolic space
本文研究二维球面超凯勒延拓在双曲圆盘上继承的复结构，证明其嵌入超凯勒流形并非全纯映射。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。