scholarly journals Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Rongsheng Ma ◽  
Donghe Pei
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformally Flat ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Generalized Sasakian Space Form ◽  
Necessary And Sufficient

In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric and their relationship between each other. As the application of our theorems, we study the Ricci almost soliton on conformally flat Lorentzian generalized Sasakian-space-form.

scholarly journals On interpolating sesqui-harmonic Legendre curves in Sasakian space forms

2019 ◽  
Vol 17 (01) ◽  
pp. 2050005 ◽  
Author(s):  
Fatma Karaca ◽  
Cihan Özgür ◽  
Uday Chand De
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Legendre Curve ◽  
Sasakian Space Forms ◽  
Legendre Curves ◽  
Necessary And Sufficient

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain a proper example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.

On pseudo-slant submanifolds of a Sasakian space form

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5909-5919
Author(s):  
Süleyman Dirik ◽  
Mehmet Atçeken ◽  
Ümit Yıldırım
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Space Forms ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Necessary And Sufficient

In this paper, we study the geometry of the pseudo-slant submanifolds of a Sasakian space form. Necessary and sufficient conditions are given for a submanifold to be pseudo-slant submanifolds, pseudo-slant product, mixed geodesic and totally geodesic in Sasakian manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifolds of Sasakian manifolds and Sasakian space forms.

scholarly journals Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dae Ho Jin
Keyword(s):  
Vector Field ◽  
Space Form ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Characterization Theorems ◽  
Lightlike Hypersurfaces

We study lightlike hypersurfacesMof an indefinite generalized Sasakian space formM-(f1,f2,f3), with indefinite trans-Sasakian structure of type(α,β), subject to the condition that the structure vector field ofM-is tangent toM. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type(α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.

scholarly journals The projective curvature of the tangent bundle with natural diagonal metric

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 401-410 ◽  
Author(s):  
Cornelia-Livia Bejan ◽  
Simona-Luiza Druţă-Romaniuc
Keyword(s):  
Riemannian Manifold ◽  
Tangent Bundle ◽  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Total Space ◽  
Projectively Flat ◽  
Projective Curvature ◽  
Necessary And Sufficient

Our study is mainly devoted to a natural diagonal metric G on the total space TMof the tangent bundle of a Riemannian manifold (M, 1). We provide the necessary and sufficient conditions under which (TM,G) is a space form, or equivalently (TM,G) is projectively Euclidean. Moreover, we classify the natural diagonal metrics G for which (TM,G) is horizontally projectively flat (resp. vertically projectively flat).

scholarly journals Inequalities on Generalized Sasakian Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Najma Abdul Rehman ◽  
Abdul Ghaffar ◽  
Esmaeil Abedi ◽  
Mustafa Inc ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Space Form ◽  
Variational Formula ◽  
Stability Criteria ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
The Stability ◽  
Second Variational Formula

In this paper, we find the second variational formula for a generalized Sasakian space form admitting a semisymmetric metric connection. Inequalities regarding the stability criteria of a compact generalized Sasakian space form admitting a semisymmetric metric connection are established.

GENERALIZED SASAKIAN SPACE FORMS WITH SEMI-SYMMETRIC METRIC CONNECTIONS

2014 ◽  
Vol 60 (1) ◽  
pp. 145-156
Author(s):  
Sibel Sular ◽  
Cihan Özgur
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Warped Products ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Generalized Sasakian Space Form

Abstract The aim of the present paper is to introduce generalized Sasakian space forms endowed with semi-symmetric metric connections. We obtain the existence theorem of a generalized Sasakian space form with semi-symmetric metric connection and we give some examples by using warped products endowed with semi-symmetric metric connection.

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.

Symmetry properties of complex contact space form

2019 ◽  
pp. 2050157 ◽  
Author(s):  
Mohamed Belkhelfa ◽  
Fatima Zohra Kadi
Keyword(s):  
Space Form ◽  
Einstein Manifold ◽  
Contact Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Symmetry Properties ◽  
Symmetric Complex ◽  
Complex Contact Manifold ◽  
Contact Space

It is well known that a Sasakian space form is pseudo-symmetric [M. Belkhelfa, R. Deszcz and L. Verstraelen, Symmetry properties of Sasakian space-forms, Soochow J. Math. 31(4) (2005) 611–616], therefore it is Ricci-pseudo-symmetric. In this paper, we proved that a normal complex contact manifold is Ricci-semi-symmetric if and only if it is an Einstein manifold; moreover, we showed that a complex contact space form [Formula: see text] with constant [Formula: see text]-sectional curvature [Formula: see text] is properly Ricci-pseudo-symmetric [Formula: see text] if and only if [Formula: see text]; in this case [Formula: see text]. We gave an example of properly Ricci-pseudo-symmetric complex contact space form. On the other hand, we proved the non-existence of proper pseudo-symmetric ([Formula: see text]) complex contact space form [Formula: see text]

scholarly journals Para-CR structures on almost paracontact metric manifolds

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Joanna Wełyczko
Keyword(s):  
Sectional Curvature ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Constant Sectional Curvature ◽  
Conformally Flat ◽  
Cr Manifolds ◽  
Cosymplectic Manifolds ◽  
Cr Structures ◽  
Necessary And Sufficient

AbstractAlmost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.

Geodesic spheres and Jacobi vector fields on Sasakian space forms

1987 ◽  
Vol 105 (1) ◽  
pp. 17-22 ◽  
Author(s):  
David E. Blair ◽  
Lieven Vanhecke
Keyword(s):  
Vector Fields ◽  
Space Form ◽  
Shape Operator ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Geodesic Spheres ◽  
Jacobi Vector

SynopsisUsing explicit equations for Jacobi vector fields on a Sasakian space form, we characterise such spaces by means of the shape operator of small geodesic spheres.

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