Related papers: Pseudo-Riemannian manifolds with recurrent spinor …

Let (M, g) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g: two almost complex and two almost product structures satisfying additionally certain integrability conditions. For instance, if r is a…

We show that a 7-dimensional non-compact Ricci-flat Riemannian manifold with Riemannian holonomy G_2 can admit non-integrable G_2 structures of type R + S^2_0(R^7) + R^7 in the sense of Fern\'andez and Gray. This relies on the construction…

We study spin structures on compact simply-connected homogeneous pseudo-Riemannian manifolds (M = G/H, g) of a compact semisimple Lie group G. We classify flag manifolds F = G/H of a compact simple Lie group which are spin. This yields also…

We introduce a notion of twisted pure spinor in order to characterize, in a unified way, all the special Riemannian holonomy groups just as a classical pure spinor characterizes the special K\"ahler holonomy. Motivated by certain curvature…

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important…

We develop the classification of weakly symmetric pseudo--riemannian manifolds $G/H$ where $G$ is a semisimple Lie group and $H$ is a reductive subgroup. We derive the classification from the cases where $G$ is compact, and then we discuss…

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…

We study curved-space rigid supersymmetry for two-dimensional $\mathcal{N}=(2,2)$ supersymmetric fields theories with a vector-like $R$-symmetry by coupling such theories to background supergravity. The associated Killing spinors can be…

Let $M$ be pseudo-Riemannian homogeneous Einstein manifold of finite volume, and suppose a connected Lie group $G$ acts transitively and isometrically on $M$. In this situation, the metric on $M$ induces a bilinear form…

We obtain the topological obstructions to existence of a bundle of irreducible real Clifford modules over a pseudo-Riemannian manifold $(M,g)$ of arbitrary dimension and signature and prove that bundles of Clifford modules are associated to…

In this paper we examine the structure of Riemannian manifolds with a special kind of Codazzi tensors. We use them to construct globally hyperbolic Lorentzian manifolds with complete Cauchy hypersurfaces for any weakly irreducible holonomy…

We classify Riemannian $\text{spin}^c$ manifolds carrying a type I imaginary generalized Killing spinor, by explicitly constructing a parallel spinor on each leaf of the canonical foliation given by the Dirac current. We also provide a…

We show that smooth type IIA Killing horizons with compact spatial sections preserve an even number of supersymmetries, and that the symmetry algebra of horizons with non-trivial fluxes includes an sl(2,R) subalgebra. This confirms the…

We show that given a conformal structure whose holonomy representation fixes a totally lightlike subspace of arbitrary dimension, there is always a local metric in the conformal class off a singular set which is Ricci-isotropic and gives…

The present paper introduces the geometry of screen generic lightlike submanifolds of a locally bronze semi-Riemannian manifolds endowed with an (l,m)-type connection. The characterization theorems on geodesicity of such submanifolds with…

The problem of classification of connected holonomy groups (equivalently of holonomy algebras) for pseudo-Riemannian manifolds is open. The classification of Riemannian holonomy algebras is a classical result. The classification of…

We study the full holonomy group of Lorentzian manifolds with a parallel null line bundle. We prove several results that are based on the classification of the restricted holonomy groups of such manifolds and provide a construction method…

The geodesic orbit property is useful and interesting in itself, and it plays a key role in Riemannian geometry. It implies homogeneity and has important classes of Riemannian manifolds as special cases. Those classes include weakly…

Let M be an oriented three-dimensional Riemannian manifold of constant sectional curvature k = 0,1,-1 and let SO(M) be its direct orthonormal frame bundle (direct refers to positive orientation), which may be thought of as the set of all…

In this paper we investigate the relationship between the existence of parallel semi-Riemannian metrics of a connection and the reducibility of the associated holonomy group. The question as to whether the holonomy group necessarily reduces…