Anti-invariant Riemannian submersions from nearly Kaehler manifolds

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.

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Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds

Filomat ◽

10.2298/fil1507429m ◽

2015 ◽

Vol 29 (7) ◽

pp. 1429-1444 ◽

Cited By ~ 6

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.

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Semi-invariant Riemannian submersions from nearly Kaehler manifolds

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820501005 ◽

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.

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

Filomat ◽

10.2298/fil1804159t ◽

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.

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Some properties of lightlike submanifolds of semi-Riemannian manifolds

Demonstratio Mathematica ◽

10.1515/dema-2013-0257 ◽

2010 ◽

Vol 43 (3) ◽

Author(s):

Rakesh Kumar ◽

Rachna Rani ◽

R. K. Nagaich

Keyword(s):

Riemannian Manifolds ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Totally Geodesic ◽

Screen Distribution ◽

Necessary And Sufficient ◽

Lightlike Submanifolds ◽

Lightlike Submanifold

AbstractWe initially obtain various relations and then establish necessary and sufficient condition for the integrability of screen distribution of a lightlike submanifold. We also establish necessary and sufficient condition for a lightlike submanifold to be totally geodesic.

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ON NON-INVARIANT HYPERSURFACES OF AN ε-PARA SASAKIAN MANIFOLD

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2001001k ◽

2020 ◽

Vol 35 (1) ◽

pp. 001

Author(s):

Shyam Kishor ◽

Prerna Kanaujia

Keyword(s):

Sasakian Manifold ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Totally Geodesic ◽

Totally Umbilical ◽

Necessary And Sufficient ◽

Induced Structure

In the present paper non-invariant hypersurfaces of an ε- para Sasakian manifold of an induced structure (f,g,u,v,λ) are studied. Some properties followed by this structure are obtained. A necessary and sufficient condition for totally umbilical non-invariant hypersurfaces equipped with (f,g,u,v,λ)- structure of ε-para Sasakian manifold to be totally geodesic has also been explored.

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TOTALLY GEODESIC SUBMANIFOLDS OF GL-MANIFOLDS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887812500028 ◽

2012 ◽

Vol 09 (01) ◽

pp. 1250002

Author(s):

ABOLGHASEM LALEH ◽

MORTEZA M. REZAII ◽

ATAABAK BAAGHERZADEH HUSHMANDI

Keyword(s):

Riemannian Manifold ◽

Finsler Manifold ◽

Finsler Metric ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Totally Geodesic ◽

Geodesic Submanifolds ◽

Totally Geodesic Submanifolds ◽

Necessary And Sufficient ◽

Sasakian Metric

In this paper, for a Finsler manifold (M, F) with a Finsler metric gij(x, y) we shall consider a generalized Lagrange metrics (FGL-metrics) as the form *gij(x, y) = gij(x, y) + σ(x, y)Bi(x, y)Bj(x, y) on TM. Then we shall consider a Riemannian manifold (TM, *G) in which *G is a generalized Sasakian metric of *g on [Formula: see text]. Then we restrict the above FGL-metrics to a submanifold of [Formula: see text], and show that it admits a GL-metric structure. Then we shall find a necessary and sufficient condition for this submanifold to be totally geodesic.

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Scalar curvature of Lagrangian Riemannian submersions and their harmonicity

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817501717 ◽

2017 ◽

Vol 14 (12) ◽

pp. 1750171 ◽

Cited By ~ 2

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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Semi-invariant Submersions from Almost Hermitian Manifolds

Canadian Mathematical Bulletin ◽

10.4153/cmb-2011-144-8 ◽

2013 ◽

Vol 56 (1) ◽

pp. 173-183 ◽

Cited By ~ 25

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.

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

Filomat ◽

10.2298/fil1810465f ◽

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

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817500748 ◽

2017 ◽

Vol 14 (05) ◽

pp. 1750074 ◽

Cited By ~ 4

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.

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