scholarly journals Riemannian submersions with totally geodesic fibers

1975 ◽  
Vol 10 (2) ◽  
pp. 253-276 ◽  
Author(s):  
Richard H. Escobales, Jr.
Keyword(s):  
Riemannian Submersions ◽  
Totally Geodesic

scholarly journals Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1429-1444 ◽  
Author(s):  
Cengizhan Murathan ◽  
Erken Küpeli
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient ◽  
Decomposition Theorems ◽  
Characteristic Vector Field

We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. We give examples of anti-invariant submersions such that characteristic vector field ? is vertical or horizontal. Moreover we give decomposition theorems by using the existence of anti-invariant Riemannian submersions.

scholarly journals Examples and classification of Riemannian submersions satisfying a basic equality

2005 ◽  
Vol 72 (3) ◽  
pp. 391-402 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Riemannian Manifold ◽  
Unit Sphere ◽  
Isometric Immersion ◽  
Riemannian Submersion ◽  
Sharp Inequality ◽  
Riemannian Submersions ◽  
Equality Case ◽  
Totally Geodesic ◽  
Basic Equality

In an earlier article we obtain a sharp inequality for an arbitrary isometric immersion from a Riemannian manifold admitting a Riemannian submersion with totally geodesic fibres into a unit sphere. In this article we investigate the immersions which satisfy the equality case of the inequality. As a by-product, we discover a new characterisation of Cartan hypersurface in S4.

scholarly journals Anti-invariant Riemannian submersions from nearly Kaehler manifolds

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1219-1235 ◽  
Author(s):  
Shahid Ali ◽  
Tanveer Fatima
Keyword(s):  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Decomposition Theorems ◽  
The Vertical Distribution

We extend the notion of anti-invariant and Langrangian Riemannian submersion to the case when the total manifold is nearly Kaehler. We obtain the integrability conditions for the horizontal distribution while it is noted that the vertical distribution is always integrable. We also investigate the geometry of the foliations of the two distributions and obtain the necessary and sufficient condition for a Langrangian submersion to be totally geodesic. The decomposition theorems for the total manifold of the submersion are obtained.

scholarly journals Laplacians and Riemannian submersions with totally geodesic fibres

1982 ◽  
Vol 26 (2) ◽  
pp. 181-200 ◽  
Author(s):  
Lionel Bérard Bergery ◽  
Jean-Pierre Bourguignon
Keyword(s):  
Riemannian Submersions ◽  
Totally Geodesic

Scalar curvature of Lagrangian Riemannian submersions and their harmonicity

2017 ◽  
Vol 14 (12) ◽  
pp. 1750171 ◽  
Author(s):  
Şemsi Eken Meri̇ç ◽  
Erol Kiliç ◽  
Yasemi̇n Sağiroğlu
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Necessary And Sufficient

In this paper, we consider a Lagrangian Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a Lagrangian Riemannian submersion [Formula: see text] has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of Lagrangian Riemannian submersions and obtain a characterization for such submersions to be harmonic.

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