scholarly journals Totally umbilical submanifolds in some semi-Riemannian manifolds

2010 ◽  
Vol 119 (2) ◽  
pp. 269-299 ◽  
Author(s):  
Stanisław Ewert-Krzemieniewski
Keyword(s):  
Riemannian Manifolds ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

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.

Conformal Killing Forms on Totally Umbilical Submanifolds

2016 ◽  
Vol 217 (5) ◽  
pp. 525-539 ◽  
Author(s):  
S. E. Stepanov ◽  
I. A. Alexandrova ◽  
I. I. Tsyganok ◽  
J. Mikeš
Keyword(s):  
Conformal Killing ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

scholarly journals Totally umbilical submanifolds of quaternion-space-forms

1978 ◽  
Vol 26 (2) ◽  
pp. 154-162 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Space Forms ◽  
Totally Umbilical ◽  
Quaternion Space ◽  
Totally Umbilical Submanifolds

AbstractTotally umbilical submanifolds of dimension greater than four in quaternion-space-forms are completely classified.

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