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 Quasi-Hemi-Slant Riemannian Submersion

2019 ◽  
pp. 1-14
Author(s):  
S. Longwap ◽  
F. Massamba ◽  
N. E. Homti
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Riemannian Submersions ◽  
Almost Hermitian Manifold ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds

We recall the notions of invariant, anti-invarian, semi-invariant, slant, semi-slant, quasi-slant and hemi-slant Riemannian submersions from almost Hermitian manifolds to a Riemannian manifolds. In this paper we contruct a Riemannian submersion which generalizes hemi-slant, semi-slant and semi-invariant Riemanian submersions from almost Hermitian manifold to a Riemannian manifold and study its geometry.

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.

scholarly journals Anti-Invariant Semi-Riemannian Submersions from Almost Para-Hermitian Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yılmaz Gündüzalp
Keyword(s):  
Riemannian Manifolds ◽  
Riemannian Submersion ◽  
Riemannian Submersions ◽  
Base Manifold ◽  
Hermitian Manifolds ◽  
Definition Of

We introduce anti-invariant semi-Riemannian submersions from almost para-Hermitian manifolds onto semi-Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a semi-Riemannian submersion, and check the harmonicity of such submersions. We also obtain curvature relations between the base manifold and the total manifold.

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.

A β-tensor on Kaehler manifolds and its geometric characterizations

2021 ◽  
pp. 2150183
Author(s):  
Şemsi Eken Meriç
Keyword(s):  
Necessary Conditions ◽  
Ricci Soliton ◽  
Hermitian Manifold ◽  
Total Space ◽  
Kaehler Manifold ◽  
Totally Geodesic ◽  
Base Manifold ◽  
Kaehler Manifolds

In this paper, we first introduce a new notion [Formula: see text]-tensor on Hermitian manifold and particularly, we present some geometric characterizations of such a tensor on the Kaehler manifold. Here, we investigate the Kaehler submersion whose total space is equipped with the [Formula: see text]-tensor and obtain some results. Also, we deal with a Kaehler submersion with totally geodesic fibers such that the total space admits [Formula: see text]-Ricci soliton and [Formula: see text]-tensor. Finally, we give necessary conditions for which any fiber and base manifold of Kaehler submersion is [Formula: see text]-Ricci soliton or [Formula: see text]-Kaehler-Einstein.

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 TANGENT BUNDLE ENDOWED WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION ON AN ALMOST HERMITIAN MANIFOLD

2020 ◽  
Vol 35 (1) ◽  
pp. 167
Author(s):  
Mohammad Nazrul Islam Khan
Keyword(s):  
Tangent Bundle ◽  
Hermitian Manifold ◽  
Nijenhuis Tensor ◽  
Kaehler Manifold ◽  
Almost Hermitian Manifold ◽  
Base Manifold ◽  
Metric Connection

In this paper, we have studied the tangent bundle endowed with quarter-symmetric non-metric connection obtained by vertical and complete lifts of a quarter-symmetric non-metric connection on the base manifold and, also, proposed the study of the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold. Finally, we obtained some theorems for Nijenhuis tensor on the tangent bundle of an almost Hermitian manifold and an almost Kaehler manifold.\\

scholarly journals On Submersion of CR-Submanifolds of l.c.q.K. Manifold

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Majid Ali Choudhary ◽  
Mahmood Jaafari Matehkolaee ◽  
Mohd. Jamali
Keyword(s):  
Riemannian Submersion ◽  
Hermitian Manifold ◽  
Kaehler Manifold ◽  
Almost Hermitian Manifold ◽  
Cr Submanifold ◽  
Locally Conformal ◽  
Cr Submanifolds

We study submersion of CR-submanifolds of an l.c.q.K. manifold. We have shown that if an almost Hermitian manifold B admits a Riemannian submersion π:M→B of a CR-submanifold M of a locally conformal quaternion Kaehler manifold M¯, then B is a locally conformal quaternion Kaehler manifold.

Riemannian submersions whose total manifolds admit a Ricci soliton

2019 ◽  
Vol 16 (12) ◽  
pp. 1950196
Author(s):  
Şemsi̇ Eken Meri̇ç ◽  
Erol Kiliç
Keyword(s):  
Necessary Conditions ◽  
Riemannian Submersion ◽  
Ricci Soliton ◽  
Riemannian Submersions ◽  
Target Manifold ◽  
Almost Ricci Soliton

In this paper, we study Riemannian submersions whose total manifolds admit a Ricci soliton. Here, we characterize any fiber of such a submersion is Ricci soliton or almost Ricci soliton. Indeed, we obtain necessary conditions for which the target manifold of Riemannian submersion is a Ricci soliton. Moreover, we study the harmonicity of Riemannian submersion from Ricci soliton and give a characterization for such a submersion to be harmonic.

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