相关论文: Pseudo-Riemannian Weakly Symmetric Manifolds

The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry…

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…

We study the geodesic orbit property for nilpotent Lie groups $N$ when endowed with a pseudo-Riemannian left-invariant metric. We consider this property with respect to different groups acting by isometries. When $N$ acts on itself by…

We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian…

In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the…

The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau \cite {Lo}) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of…

To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.

It is shown that in the weak field approximation the new geometrical approach can lead to the linear field equations for the several independent fields. For the stronger fields and in the second order approximation the field equations…

In this paper we prove that every locally minimizing curve with constant speed in a prox-regular subset of a Riemannian manifold is a weak geodesic. Moreover, it is shown that under certain assumptions, every weak geodesic is locally…

A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.

For $n\geq 4$ we show that generic closed Riemannian $n$-manifolds have no nontrivial totally geodesic submanifolds, answering a question of Spivak. An immediate consequence is a severe restriction on the isometry group of a generic…

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.

$\Gamma$-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting $\Gamma$-structures are free over odd degree generators. We prove that this…

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong…

We prove that the tangent bundle of an inner symmetric space $M$ of compact type is weakly complex if and only if $M$ is a Riemannian product $M_1\times...\times M_k$, each $M_i$ being an even-dimensional round sphere or Hermitian…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from CR manifolds into Riemannian manifolds or Kahler manifolds. Some basicity, pluriharmonicity and Siu-Sampson type results are established for both…

Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),\xi)$-semi-Riemannian manifolds are classified. Some results for ${\cal…