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

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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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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Anti-invariant Riemannian submersions from nearly Kaehler manifolds

Filomat ◽

10.2298/fil1307219a ◽

2013 ◽

Vol 27 (7) ◽

pp. 1219-1235 ◽

Cited By ~ 6

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.

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Anti-invariant Riemannian submersions from Sasakian manifolds with totally umbilical fibers

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887821501693 ◽

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.

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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 the Differential Equation Governing Torqued Vector Fields on a Riemannian Manifold

Symmetry ◽

10.3390/sym12121941 ◽

2020 ◽

Vol 12 (12) ◽

pp. 1941

Author(s):

Sharief Deshmukh ◽

Nasser Bin Turki ◽

Haila Alodan

Keyword(s):

Riemannian Manifold ◽

Vector Field ◽

Euclidean Space ◽

Riemannian Manifolds ◽

Vector Fields ◽

Compact Riemannian Manifold ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Rigidity Results ◽

Necessary And Sufficient

In this article, we show that the presence of a torqued vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian manifolds of constant curvature. More precisely, we show that there is no torqued vector field on n-sphere Sn(c). A nontrivial example of torqued vector field is constructed on an open subset of the Euclidean space En whose torqued function and torqued form are nowhere zero. It is shown that owing to topology of the Euclidean space En, this type of torqued vector fields could not be extended globally to En. Finally, we find a necessary and sufficient condition for a torqued vector field on a compact Riemannian manifold to be a concircular vector field.

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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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Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds

10.20944/preprints202106.0622.v1 ◽

2021 ◽

Author(s):

Hristo Manev ◽

Mancho Manev

Keyword(s):

Vector Field ◽

Riemannian Manifolds ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Reeb Vector ◽

Reeb Vector Field ◽

Special Cases ◽

Necessary And Sufficient

It is introduced and studied para-Ricci-like solitons with potential Reeb vector field on almost paracontact almost paracomplex Riemannian manifolds. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field have been considered. It is proved a necessary and sufficient condition the manifold to admit a para-Ricci-like soliton which is the structure to be para-Einstein-like. Explicit examples are provided in support of the proven statements.

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Bakry-Émery Conditions on Almost Smooth Metric Measure Spaces

Analysis and Geometry in Metric Spaces ◽

10.1515/agms-2018-0007 ◽

2018 ◽

Vol 6 (1) ◽

pp. 129-145 ◽

Cited By ~ 2

Author(s):

Shouhei Honda

Keyword(s):

Riemannian Manifolds ◽

Short Note ◽

Sufficient Condition ◽

Metric Measure Spaces ◽

Necessary And Sufficient Condition ◽

Local Dimension ◽

Base Points ◽

Smooth Metric Measure Spaces ◽

Measure Spaces ◽

Necessary And Sufficient

Abstract In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K, N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells us that the BE condition is strictly weaker than the RCD condition even in this setting, and that the local dimension is not constant even if the space satisfies the BE condition with the coincidence between the induced distance by the Cheeger energy and the original distance. In particular, the glued space gives a first example with a Ricci bound from below in the Bakry-Émery sense, whose local dimension is not constant. We also give a necessary and sufficient condition for such spaces to be RCD(K, N) spaces.

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