Bi-conformal vector fields and the local geometric characterization of conformally separable (double-twisted) pseudo-Riemannian manifolds

Bi-conformal vector fields and their applications to the characterization of conformally separable pseudo-Riemannian manifolds: New criteria for the existence of conformally flat foliations in pseudo-Riemannian manifolds

In this paper a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.}\textbf{21}, 2153-2177 and some of their basic properties were addressed there. Bi-conformal vector fields are defined on a pseudo-Riemannian manifold through the differential conditions $\lie P_{ab}=ϕP_{ab}$ and $\lieΠ_{ab}=χΠ_{ab}$ where $P_{ab}$ and $Π_{ab}$ are orthogonal and complementary projectors with respect to the metric tensor $\rmg_{ab}$. One of the main re…

Bi-conformal vector fields and the local geometric characterization of conformally separable pseudo-Riemannian manifolds II

In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=ϕP_{ab}$, $\lieΠ_{ab}=χΠ_{ab}$ where $P_{ab}$, $Π_{ab}$ are orthogonal and complementary projectors with respect to the metric tensor $\rmg_{ab}$ and $\lie$ is the Lie derivative. In a previous paper we explained how the analysis of these differential conditions enabled us to derive local geometric characterizations of the most relevant cases of {\em conformally sep…

Osserman and conformally Osserman manifolds with warped and twisted product structure

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature.

局部共形Kähler流形上扭曲Hamiltonian向量场的矩映射

A moment map for twisted-Hamiltonian vector fields on locally conformally Kähler manifolds

本文将Kähler几何中标量曲率作为矩映射的经典Donaldson-Fujiki解释推广至局部共形Kähler几何框架。

Locally conformally symplectic convexity

We investigate special lcs and twisted Hamiltonian torus actions on strict lcs manifolds and characterize them geometrically in terms of the minimal presentation. We prove a convexity theorem for the corresponding twisted moment map, establishing thus an analog of the symplectic convexity theorem of Atiyah and Guillemin-Sternberg. We also prove similar results for the symplectic moment map (defined on the minimal presentation) whose image is then a convex cone. In the special case of a compact toric Vaisman manifold, we obtain a structure theorem.

Twisted differentials and Lee classes of locally conformally symplectic complex surfaces

We study the set of deRham classes of Lee $1$-forms of the locally conformally symplectic (LCS) structures taming the complex structure of a compact complex surface in the Kodaira class VII, and show that the existence of non-trivial upper/lower bounds with respect to the degree function correspond respectively to the existence of certain negative/non-negative PSH functions on the universal cover. We use this to prove that the set of Lee deRham classes of taming LCS is connected, as well as to obtain an explicit negative upper bound for this set on the hyperbolic Kato surfaces. This leads to a…