scholarly journals On some types of lightlike submanifolds of golden semi-Riemannian manifolds

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3231-3242
Author(s):  
Feyza Erdoğan
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Metric Connection ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds

The main purpose of the present paper is to study the geometry of screen transversal lightlike submanifolds and radical screen transversal lightlike submanifolds and screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. We investigate the geometry of distributions and obtain necessary and sufficient conditions for the induced connection on these manifolds to be metric connection. We also obtain characterizations of screen transversal anti-invariant lightlike submanifolds of Golden semi-Riemannian manifolds. Finally, we give two examples.

SEMI-INVARIANT RIEMANNIAN MAPS TO KÄHLER MANIFOLDS

2011 ◽  
Vol 08 (07) ◽  
pp. 1439-1454 ◽  
Author(s):  
BAYRAM ṢAHIN
Keyword(s):  
Riemannian Manifolds ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
Necessary And Sufficient Conditions ◽  
Classification Theorem ◽  
Totally Geodesic ◽  
Hermitian Manifolds ◽  
Almost Hermitian Manifolds ◽  
Riemannian Map ◽  
Necessary And Sufficient

This paper has two aims. First, we show that the usual notion of umbilical maps between Riemannian manifolds does not work for Riemannian maps. Then we introduce a new notion of umbilical Riemannian maps between Riemannian manifolds and give a method on how to construct examples of umbilical Riemannian maps. In the second part, as a generalization of CR-submanifolds, holomorphic submersions, anti-invariant submersions, invariant Riemannian maps and anti-invariant Riemannian maps, we introduce semi-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples and investigate the geometry of distributions which are arisen from definition. We also obtain a decomposition theorem and give necessary and sufficient conditions for a semi-invariant Riemannian map to be totally geodesic. Then we study the geometry of umbilical semi-invariant Riemannian maps and obtain a classification theorem for such Riemannian maps.

Biharmonic submanifolds in metallic Riemannian manifolds

2021 ◽  
Author(s):  
Mohamd Saleem Lone ◽  
Siraj Uddin ◽  
Mohammad Hasan Shahid
Keyword(s):  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Biharmonic Submanifolds ◽  
Complex Surfaces ◽  
Metallic Structures ◽  
Necessary And Sufficient

In this paper, we study the biharmonic submanifolds of Riemannian manifolds endowed with metallic and complex metallic structures. In case of both the structures, we obtain the necessary and sufficient conditions for a submanifold to be biharmonic. Particularly, we find the estimates for mean curvature of Lagrangian and complex surfaces.

scholarly journals Biharmonic submanifolds in3-dimensional(κ,μ)-manifolds

2005 ◽  
Vol 2005 (22) ◽  
pp. 3575-3586 ◽  
Author(s):  
K. Arslan ◽  
R. Ezentas ◽  
C. Murathan ◽  
T. Sasahara
Keyword(s):  
Riemannian Manifolds ◽  
Critical Points ◽  
Harmonic Maps ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Biharmonic Maps ◽  
Biharmonic Submanifolds ◽  
Invariant Surfaces ◽  
Legendre Curves ◽  
Necessary And Sufficient

Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of3-dimensional(κ,μ)-manifolds to be biharmonic.

scholarly journals Integrability of distributions in CR-lightlike submanifolds

2002 ◽  
Vol 33 (3) ◽  
pp. 209-222
Author(s):  
Bayram Sahin ◽  
Rifat Gunes
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we study CR-lighlike submanifolds of an indefinite Kaehler manifold. Integrability of distributions on CR-lightlike submanifold investigated. We give some necessary and sufficient conditions on integrability of distibutions on CR-lightlike submanifolds in an indefinite Kaehler manifolds.

On the geometry of screen conformal submersions of semi-transversal lightlike submanifolds

2020 ◽  
pp. 2150133
Author(s):  
Rupali Kaushal ◽  
Rakesh Kumar ◽  
Rakesh Kumar Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds

We study screen conformal lightlike submersions of semi-transversal lightlike submanifolds of indefinite Kaehler manifolds, which can be considered as a lightlike version of horizontally conformal submersions. We establish necessary and sufficient conditions for a screen conformal lightlike submersion to be harmonic.

scholarly journals GCR-Lightlike Product of Indefinite Sasakian Manifolds

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Rakesh Kumar ◽  
Varun Jain ◽  
R. K. Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We study mixed geodesicGCR-lightlike submanifolds of indefinite Sasakian manifolds and obtain some necessary and sufficient conditions for aGCR-lightlike submanifold to be aGCR-lightlike product.

scholarly journals GCR-Lightlike Product of Indefinite Kaehler Manifolds

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Rakesh Kumar ◽  
Sangeet Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Kaehler Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We study geodesic -lightlike submanifolds of indefinite Kaehler manifolds and obtain some necessary and sufficient conditions for a -lightlike submanifold to be a -lightlike product.

scholarly journals Slant lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 277-287 ◽  
Author(s):  
Bayram Sahin ◽  
Cumali Yıldırım
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

In this paper, we define and study both slant lightlike submanifolds and screen slant lightlike submanifolds of an indefinite Sasakian manifold. We provide non-trivial examples and obtain necessary and sufficient conditions for the existence of a slant lightlike submanifold.

scholarly journals Radical transversal SCR-lightlike submanifolds of indefinite Sasakian manifolds

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2585-2594
Author(s):  
S.S. Shukla ◽  
Akhilesh Yadav
Keyword(s):  
Sufficient Conditions ◽  
Characterization Theorem ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Manifolds ◽  
Totally Geodesic ◽  
Integrability Conditions ◽  
Cauchy Riemann ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds

In this paper, we introduce the notion of radical transversal screen Cauchy-Riemann (SCR)- lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some nontrivial examples of such submanifolds. Integrability conditions of distributions D1, D2, D and D? on radical transversal SCR-lightlike submanifolds of an indefinite Sasakian manifold have been obtained. Further, we obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

scholarly journals Invariant submanifolds of generalized Sasakian-space-forms

2018 ◽  
Vol 15 (09) ◽  
pp. 1850149 ◽  
Author(s):  
Shyamal Kumar Hui ◽  
Siraj Uddin ◽  
ALi H. Alkhaldi ◽  
Pradip Mandal
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Ricci Solitons ◽  
Space Forms ◽  
Totally Geodesic ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Invariant Submanifolds ◽  
Levi Civita Connection ◽  
Necessary And Sufficient

This paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide an example of such submanifolds and obtain many new results including the necessary and sufficient conditions under which the submanifolds are totally geodesic. The Ricci solitons of such submanifolds are also studied.

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