scholarly journals Conformally Flat Totally Umbilical Submanifolds in Some Semi-Riemannian Manifolds

2008 ◽  
Vol 48 (2) ◽  
pp. 183-194 ◽  
Author(s):  
Stanislaw Ewert-Krzemieniewski
Keyword(s):  
Riemannian Manifolds ◽  
Conformally Flat ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

scholarly journals $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

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.

Geometries and Topologies of Conformally Flat Riemannian Manifolds

2020 ◽  
Vol 46 (6) ◽  
pp. 1683-1695
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifolds ◽  
Conformally Flat
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