scholarly journals On complete totally umbilical and maximal space-like surfaces in pseudo-Riemannian manifolds

2013 ◽  
Vol 14 (2) ◽  
pp. 613 ◽  
Author(s):  
Irina I. Tsyganok ◽  
Sergey E. Stepanov
Keyword(s):  
Riemannian Manifolds ◽  
Totally Umbilical ◽  
Maximal Space

Anti-invariant Riemannian submersions from Sasakian manifolds with totally umbilical fibers

2021 ◽  
pp. 2150169
Author(s):  
Gizem Köprülü ◽  
Bayram Şahin
Keyword(s):  
Vector Field ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Sasakian Manifold ◽  
Riemannian Submersion ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Totally Umbilical ◽  
Characteristic Vector Field ◽  
Horizontal Vector

The purpose of this paper is to study anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds such that characteristic vector field is vertical or horizontal vector field. We first show that any anti-invariant Riemannian submersions from Sasakian manifold is not a Riemannian submersion with totally umbilical fiber. Then we introduce anti-invariant Riemannian submersions from Sasakian manifolds with totally contact umbilical fibers. We investigate the totally contact geodesicity of fibers of such submersions. Moreover, under this condition, we investigate Ricci curvature of anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds.

A remark on the mixed scalar curvature of a manifold with two orthogonal totally umbilical distributions

2019 ◽  
Vol 19 (3) ◽  
pp. 291-296 ◽  
Author(s):  
Sergey Stepanov ◽  
Irina Tsyganok
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Type Theorem ◽  
Complete Riemannian Manifold ◽  
Warped Products ◽  
Liouville Type ◽  
Liouville Type Theorem ◽  
Totally Umbilical

Abstract We prove a Liouville-type theorem for two orthogonal complementary totally umbilical distributions on a complete Riemannian manifold with non-positive mixed scalar curvature. This is applied to some special types of complete doubly twisted and warped products of Riemannian manifolds.

On the Three-Dimensional Homogenous SO(2)-Isotropic Riemannian Manifolds

2011 ◽  
Vol 57 (2) ◽  
pp. 361-376
Author(s):  
P. Piu ◽  
M. Profir
Keyword(s):  
Riemannian Manifolds ◽  
Three Dimensional ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Geodesic Surfaces ◽  
Rotational Surfaces

On the Three-Dimensional Homogenous SO(2)-Isotropic Riemannian Manifolds In this paper we consider some properties of the three-dimensional homogenous SO(2)-isotropic Riemannian manifolds. In particular, we determine the geodesics, the totally geodesic surfaces, the totally umbilical surfaces and the geodesics of the rotational surfaces.

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