Related papers: On the normal holonomy representation of spacelike…
We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal…
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…
This article investigates the holonomy groups of K-contact sub-pseudo-Riemannian manifolds. The primary result is a proof that the horizontal holonomy group either coincides with the adapted holonomy group or acts as its normal subgroup of…
The classification of the holonomy algebras of Lorentzian manifolds can be reduced to the classification of irreducible subalgebras $\mathfrak{h}\subset\mathfrak{so}(n)$ that are spanned by the images of linear maps from $\mathbb{R}^n$ to…
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…
The object of this article is to compute the holonomy group of the normal connection of complex parallel submanifolds of the complex projective space. We also give a new proof of the classification of complex parallel submanifolds by using…
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…
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 study the holonomy that is associated to a sub-Riemannian structure defined on the kernel of a global contact form. This includes the holonomy of Schouten's horizontal connection as well as of the adapted connection, both canonical…
The classification of 4-dimensional naturally reductive pseudo-Riemannian spaces is given. This classification comprises symmetric spaces, the product of 3-dimensional naturally reductive spaces with the real line and new families of…
In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…
We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.
We present an approach to solvable pseudo-Riemannian symmetric spaces based on papers of M.Cahen, M.Parker and N.Wallach. Thereby we reproduce the classification of solvable symmetric triples of Lorentzian signature $(1,n-1)$ and complete…
The classification problem for holonomy of pseudo-Riemannian manifolds is actual and open. In the present paper, holonomy algebras of Lorentz-K\"ahler manifolds are classified. A simple construction of a metric for each holonomy algebra is…
Degenerate submanifolds of pseudo-Riemannian manifolds are quite difficult to study because there is no prefered connection when the submanifold is not totally geodesic. For the particular case of degenerate totally umbilical hypersurfaces,…
The local classification of conformally flat Lorentzian manifolds with special holonomy groups is obtained. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.
In this paper we give a spinorial representation of submanifolds of any dimension and codimension into Riemannian space forms in terms of the existence of so called generalized Killing spinors. We then discuss several applications, among…
There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses.…
We classify homogeneous pseudo-Riemannian manifolds of index 4 which admit an invariant almost hyper-Hermitian structure and an H-irreducible isotropy group. The main result is that all these spaces are flat except in dimension 12.
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…