Related papers: Pseudo-Riemannian Weakly Symmetric Manifolds
The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the…
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 homogeneous geodesics of sub-Riemannian manifolds, i.e., normal geodesics that are orbits of one-parametric subgroups of isometries. We obtain a criterion for a geodesic to be homogeneous in terms of its initial momentum. We prove…
In this survey, symmetry provides a framework for classification of manifolds with differential-geometric structures. We highlight pseudo-Riemannian metrics, conformal structures, and projective structures. A range of techniques have been…
Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $\Phi\colon X\to Y$. We find a structural characteristic of finite…
Using Rauch's comparison theorem, we prove several monotonicity inequalities for Riemannian submanifolds. Our main result is a general Li-Yau inequality which is applicable in any Riemannian manifold whose sectional curvature is bounded…
In this work we discuss the notion of stationary curves of the length functional, the so-called (weak) geodesics, on a Riemannian manifold. The motivation behind this work is to give a detailed description of many key concepts from…
Our aim in this paper is to investigate some types of lightlike submanifolds in metallic semi-Riemannian manifolds. We study invariant and screen semi-invariant lightlike submanifolds of metallic semi-Riemannian manifolds and give examples.…
These are lecture notes on the rigidity of submanifolds of projective space "resembling" compact Hermitian symmetric spaces in their homogeneous embeddings. Recent results are surveyed, along with their classical predecessors. The notes…
In this paper we study weakly irreducible holonomy representations of the normal connection of a spacelike submanifold in a pseudo-Riemannian space from. We associate screen representations to weakly irreducible normal holonomy groups and…
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 purpose of this note is to prove the existence of global weak solutions to the flow associated to integro-differential harmonic maps into spheres and Riemannian homogeneous manifolds.
In this thesis, we study extensions of the theory of Riemannian submanifolds in two directions. First, we will show how Riemannian geometry and submanifold theory in particular, can be generalized using the notion of 'Rinehart spaces', and…
We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.
We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the…
The aim of our paper is to focus on some properties of slant and semi-slant submanifolds of metallic Riemannian manifolds. We give some characterizations for submanifolds to be slant or semi-slant submanifolds in metallic or Golden…
We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…
This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannain situation;…
This research work introduces the structure of invariant and screen semi-invariant lightlike submanifolds of a metallic semi-Riemannian manifold with a quarter symmetric non-metric connection, elaborated with examples. It delves into the…
Harvey-Lawson and Anciaux introduced the notion of austere submanifolds in pseudo-Riemannian geometry. We give an equivalent condition for an orbit of the isotropy representations for semisimple pseudo-Riemannian symmetric space to be an…