Related papers: Conformally flat Lorentzian manifolds with special…

We show that the holonomy group of a connected Riemannian locally symmetric space (not necessarily complete) without local flat factor is compact and has finite index in its normalizer in the orthogonal group.

This is a survey article on the existence of locally conformally flat(LCF) and self-dual(SD) metrics on various basic 4-manifolds like simply-connected ones or product types

We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated…

We consider four dimensional conformally flat homogeneous pseudo Riemannian manifolds. According to forms (Seger types) of the Ricci operator, we provide a full classification of four dimensional pseudo Riemannian conformally flat…

For a conformal vector field on a closed, real-analytic, Lorentzian manifold we prove that the flow is locally isometric -- that it preserves a metric in the conformal class on a neighborhood of any point -- or the metric is everywhere…

In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In…

We approach the problem of finding obstructions to curvature distinguished Riemannian metrics by considering Lorentzian metrics to which they are dual in a suitable sense. Obstructions to the latter then yield obstructions to the former.…

In this paper, we investigate complete curvature-adapted submanifolds with maximal flat section and trivial normal holonomy group in symmetric spaces of compact type or non-compact type under certain condition, and derive the constancy of…

In 1995, S. Adams and G. Stuck as well as A. Zeghib independently provided a classification of non-compact Lie groups which can act isometrically and locally effectively on compact Lorentzian manifolds. In the case that the corresponding…

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension $n\geq 3$ is locally a warped product with $(n-1)$-dimensional fibers of constant curvature. This result includes also the case of…

We prove that a four-dimensional Lorentzian manifold that is curvature homogeneous of order 3, or $\CH_3$ for short, is necessarily locally homogeneous. We also exhibit and classify four-dimensional Lorentzian, $\CH_2$ manifolds that are…

We consider pointed Lorentzian manifolds and construct "canonical" foliations by constant mean curvature (CMC) hypersurfaces. Our result assumes a uniform bound on the local sup-norm of the curvature of the manifold and on its local…

We prove that each special Lorentzian holonomy group (with the exception of those including the isotropy groups of K\"ahler symmetric spaces with rank greater than one) can be realized as the holonomy group of a globally hyperbolic…

We show that Lorentzian manifolds whose isometry group is of dimension at least $\frac{1}{2}n(n-1)+1$ are expanding, steady and shrinking Ricci solitons and steady gradient Ricci solitons. This provides examples of complete locally…

We prove that the normal metric contact pairs with orthogonal characteristic foliations, which are either Bochner flat or locally conformally flat, are locally isometric to the Hopf manifolds. As a corollary we obtain the classification of…

We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one…

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of…

Supersymmetric solutions of supergravity theories, and consequently metrics with special holonomy, have played an important role in the development of string theory. We describe how a Lorentzian manifold is either completely reducible, and…

We compute the full holonomy group of compact Lorentzian manifolds with parallel Weyl tensor, which are neither conformally flat nor locally symmetric, for the case where the fundamental group is contained in a distinguished subgroup G of…