scholarly journals Generic riemannian submersions

2013 ◽  
Vol 44 (4) ◽  
pp. 395-409 ◽  
Author(s):  
Tanveer Fatima ◽  
Shahid Ali
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Generic Product ◽  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Almost Hermitian Manifold ◽  
Definition Of ◽  
Necessary And Sufficient

B. Sahin [12] introduced the notion of semi-invariant Riemannian submersions as a generalization of anti-invariant Riemmanian submersions [11]. As a generalization to semi-invariant Riemannian submersions we introduce the notion of generic submersion from an almost Hermitian manifold onto a Riemannian manifold and investigate the geometry of foliations which arise from the definition of a generic Riemannian submersion and find necessary and sufficient condition for total manifold to be a generic product manifold. We also find necessary and sufficient conditions for a generic submersion to be totally geodesic.

scholarly journals Semi-invariant Riemannian submersions from nearly Kaehler manifolds

2020 ◽  
Vol 17 (07) ◽  
pp. 2050100
Author(s):  
Rupali Kaushal ◽  
Rashmi Sachdeva ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Horizontal Distribution ◽  
Product Manifold ◽  
Riemannian Submersions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Nearly Kaehler Manifold ◽  
The Vertical Distribution ◽  
Usual Product

We study semi-invariant Riemannian submersions from a nearly Kaehler manifold to a Riemannian manifold. It is well known that the vertical distribution of a Riemannian submersion is always integrable therefore, we derive condition for the integrability of horizontal distribution of a semi-invariant Riemannian submersion and also investigate the geometry of the foliations. We discuss the existence and nonexistence of semi-invariant submersions such that the total manifold is a usual product manifold or a twisted product manifold. We establish necessary and sufficient conditions for a semi-invariant submersion to be a totally geodesic map. Finally, we study semi-invariant submersions with totally umbilical fibers.

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.

scholarly journals Semi-invariant Submersions from Almost Hermitian Manifolds

2013 ◽  
Vol 56 (1) ◽  
pp. 173-183 ◽  
Author(s):  
Bayram Ṣahin
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Definition Of ◽  
Necessary And Sufficient

AbstractWe introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semiinvariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.

Semi-invariant ξ⊥-Riemannian submersions from almost contact metric manifolds

2017 ◽  
Vol 14 (05) ◽  
pp. 1750074 ◽  
Author(s):  
Mehmet Akif Akyol ◽  
Ramazan Sarı ◽  
Elif Aksoy
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Almost Contact Metric Manifolds

As a generalization of anti-invariant [Formula: see text]-Riemannian submersions, we introduce semi-invariant [Formula: see text]-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We give examples, investigating the geometry of foliations which arise from the definition of a Riemannian submersion and proving a necessary and sufficient condition for a semi-invariant [Formula: see text]-Riemannian submersion to be totally geodesic. Moreover, we study semi-invariant [Formula: see text]-Riemannian submersions with totally umbilical fibers.

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 Hemi-slant ξ⊥-Riemannian submersions in contact geometry

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3747-3758
Author(s):  
Ramazan Sari ◽  
Mehmet Akyol
Keyword(s):  
Riemannian Manifolds ◽  
Natural Generalization ◽  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Space Forms ◽  
Base Manifold ◽  
Sasakian Space Forms ◽  
Necessary And Sufficient

M. A. Akyol and R. Sar? [On semi-slant ??-Riemannian submersions, Mediterr. J. Math. 14(6) (2017) 234.] defined semi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant ??-Riemannian submersions, semi-invariant ??-Riemannian submersions and slant submersions, we study hemi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to be a locally product manifold. Moreover, we obtain some curvature relations from Sasakian space forms between the total space, the base space and the fibres.

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 Anti-invariant Riemanian submersions from nearly-k-cosymplectic manifolds

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1159-1174
Author(s):  
Ju Tan ◽  
Na Xu
Keyword(s):  
Vector Field ◽  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Riemannian Submersions ◽  
Totally Geodesic ◽  
Cosymplectic Manifolds ◽  
Necessary And Sufficient ◽  
Characteristic Vector Field

In this paper, we introduce anti-invariant Riemannian submersions from nearly-K-cosymplectic manifolds onto Riemannian manifolds. We study the integrability of horizontal distributions. And we investigate the necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and harmonic. Moreover, we give examples of anti-invariant Riemannian submersions such that characteristic vector field ? is vertical or horizontal.

scholarly journals Contact-Complex Riemannian Submersions

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 2996
Author(s):  
Cornelia-Livia Bejan ◽  
Şemsi Eken Meriç ◽  
Erol Kılıç
Keyword(s):  
Riemannian Submersion ◽  
Ricci Soliton ◽  
Hermitian Manifold ◽  
Horizontal Distribution ◽  
The Other ◽  
Riemannian Submersions ◽  
Almost Hermitian Manifold ◽  
Base Manifold ◽  
Contact Complex ◽  
Contact Riemannian Manifold

A submersion from an almost contact Riemannian manifold to an almost Hermitian manifold, acting on the horizontal distribution by preserving both the metric and the structure, is, roughly speaking a contact-complex Riemannian submersion. This paper deals mainly with a contact-complex Riemannian submersion from an η-Ricci soliton; it studies when the base manifold is Einstein on one side and when the fibres are η-Einstein submanifolds on the other side. Some results concerning the potential are also obtained here.

scholarly journals On anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds

Filomat ◽  
2018 ◽  
Vol 32 (10) ◽  
pp. 3465-3478
Author(s):  
Morteza Faghfouri ◽  
Sahar Mashmouli
Keyword(s):  
Vector Field ◽  
Sufficient Conditions ◽  
Riemannian Submersion ◽  
Lorentzian Manifolds ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Contact Manifolds ◽  
Necessary And Sufficient ◽  
Decomposition Theorems ◽  
Characteristic Vector Field

In this paper, we study a semi-Riemannian submersion from Lorentzian almost (para) contact manifolds and find necessary and sufficient conditions for the characteristic vector field to be vertical or horizontal. We also obtain decomposition theorems for anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds onto Lorentzian manifolds.

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