scholarly journals A characterization of minimal ascreen null hypersurfaces of $(LCS)$-space forms

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Constant Curvature ◽  
Ricci Tensor ◽  
Space Form ◽  
Null Hypersurface ◽  
Space Forms ◽  
Screen Distribution ◽  
Null Hypersurfaces ◽  
Null Curve

In the present paper, we study nontotally geodesic minimal ascreen null hypersurface, $M$, of a Lorentzian concircular structure $(LCS)$-space form of constant curvature $0$ or $1$. We prove that; if the Ricci tensor of $M$ is parallel with respect to any leaf of its screen distribution, then $M$ is isometric to a product of a null curve and spheres.

scholarly journals On Einstein null hypersurfaces of $(LCS)_{n+2}$-space forms

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Ricci Tensor ◽  
Null Hypersurface ◽  
Space Forms ◽  
Null Hypersurfaces ◽  
Geometric Conditions ◽  
Null Curves ◽  
Products Of Spheres

We show that ascreen null hypersurfaces of an $(n+2)$-dimensional Lorentzian concircular structure $(LCS)_{n+2}$-manifold admits an induced Ricci tensor. We, therefore, prove, under some geometric conditions, that an Einstein ascreen null hypersurface is locally a product of null curves and products of spheres.

scholarly journals A Characterization of Ruled Real Hypersurfaces in Non-Flat Complex Space Forms

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 642
Author(s):  
George Kaimakamis ◽  
Konstantina Panagiotidou ◽  
Juan de Dios Pérez
Keyword(s):  
Ricci Tensor ◽  
Complex Space ◽  
Space Form ◽  
Flat Space ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Ruled Real Hypersurfaces ◽  
Levi Civita Connection ◽  
Complex Space Forms

The Levi-Civita connection and the k-th generalized Tanaka-Webster connection are defined on a real hypersurface M in a non-flat complex space form. For any nonnull constant k and any vector field X tangent to M the k-th Cho operator F X ( k ) is defined and is related to both connections. If X belongs to the maximal holomorphic distribution D on M, the corresponding operator does not depend on k and is denoted by F X and called Cho operator. In this paper, real hypersurfaces in non-flat space forms such that F X S = S F X , where S denotes the Ricci tensor of M and a further condition is satisfied, are classified.

A Characterization of Real Hypersurfaces in Complex Space Forms in Terms of the Ricci Tensor

1997 ◽  
Vol 40 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Christos Baikoussis
Keyword(s):  
Ricci Tensor ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Space Forms ◽  
Complex Space Forms ◽  
Orthogonal Distribution

AbstractWe study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T0.

Chen-like inequalities on null hypersurfaces with closed rigging of a Lorentzian manifold

2021 ◽  
pp. 2150125
Author(s):  
Amrinder Pal Singh ◽  
Cyriaque Atindogbe ◽  
Rakesh Kumar ◽  
Varun Jain
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Lorentzian Manifold ◽  
Null Hypersurface ◽  
Lorentzian Space ◽  
Null Hypersurfaces

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

scholarly journals QUASI-CONFORMAL CURVATURE TENSOR OF GENERALIZED SASAKIAN-SPACE-FORMS

2020 ◽  
Vol 35 (1) ◽  
pp. 089
Author(s):  
Braj B. Chaturvedi ◽  
Brijesh K. Gupta
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Space Form ◽  
Riemannian Curvature ◽  
Space Forms ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Sasakian Space Forms ◽  
Riemannian Curvature Tensor

The present paper deals the study of generalised Sasakian-space-forms with the conditions Cq(ξ,X).S = 0, Cq(ξ,X).R = 0 and Cq(ξ,X).Cq = 0, where R, S and Cq denote Riemannian curvature tensor, Ricci tensor and quasi-conformal curvature tensor of the space-form, respectively and at last, we have given some examples to improve our results.

scholarly journals Characterization of Skew CR-Warped Product Submanifolds in Complex Space Forms via Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ibrahim Al-Dayel ◽  
Meraj Ali Khan
Keyword(s):  
Euclidean Space ◽  
Differential Equations ◽  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Geometric Conditions ◽  
Complex Space Forms ◽  
The Impact

Recently, we have obtained Ricci curvature inequalities for skew CR-warped product submanifolds in the framework of complex space form. By the application of Bochner’s formula on these inequalities, we show that, under certain conditions, the base of these submanifolds is isometric to the Euclidean space. Furthermore, we study the impact of some differential equations on skew CR-warped product submanifolds and prove that, under some geometric conditions, the base is isometric to a special type of warped product.

Curvature of Cr Manifolds

2013 ◽  
Vol 59 (1) ◽  
pp. 43-72
Author(s):  
Aurel Bejancu ◽  
Hani Reda Farran
Keyword(s):  
Existence And Uniqueness ◽  
Ricci Tensor ◽  
Tensor Field ◽  
Differential Operators ◽  
Linear Connection ◽  
Horizontal Distribution ◽  
Einstein Equations ◽  
Space Forms ◽  
Torsion Free

Abstract We prove the existence and uniqueness of a torsion-free and h-metric linear connection ▽(CR connection) on the horizontal distribution of a CR manifold M. Then we define the CR sectional curvature of M and obtain a characterization of the CR space forms. Also, by using the CR Ricci tensor and the CR scalar curvature we define the CR Einstein gravitational tensor field on M. Thus, we can write down Einstein equations on the horizontal distribution of the 5-dimensional CR manifold involved in the Penrose correspondence. Finally, some CR differential operators are defined on M and two examples are given to illustrate the theory developed in the paper. Most of the results are obtained for CR manifolds that do not satisfy the integrability conditions

scholarly journals On 3-Dimensional Contact Metric Generalized(k,μ)-Space Forms

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
D. G. Prakasha ◽  
Shyamal Kumar Hui ◽  
Kakasab Mirji
Keyword(s):  
Constant Curvature ◽  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Forms ◽  
3 Dimensional ◽  
Projectively Flat ◽  
Necessary And Sufficient

The present paper deals with a study of 3-dimensional contact metric generalized(k,μ)-space forms. We obtained necessary and sufficient condition for a 3-dimensional contact metric generalized(k,μ)-space form withQϕ=ϕQto be of constant curvature. We also obtained some conditions of such space forms to be pseudosymmetric andξ-projectively flat, respectively.

scholarly journals CR-Submanifolds of Generalized -Space Forms

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Mahmood Jaafari Matehkolaee
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Upper Bound ◽  
Ricci Tensor ◽  
Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Cr Submanifold ◽  
Special Cases ◽  
Cr Submanifolds

We study sectional curvature, Ricci tensor, and scalar curvature of submanifolds of generalized -space forms. Then we give an upper bound for foliate -horizontal (and vertical) CR-submanifold of a generalized -space form and an upper bound for minimal -horizontal (and vertical) CR-submanifold of a generalized -space form. Finally, we give the same results for special cases of generalized -space forms such as -space forms, generalized Sasakian space forms, Sasakian space forms, Kenmotsu space forms, cosymplectic space forms, and almost -manifolds.

scholarly journals Geometry of isoparametric null hypersurfaces of Lorentzian manifolds

2019 ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Ambient Space ◽  
Null Hypersurface ◽  
Principal Curvatures ◽  
Lorentzian Manifolds ◽  
Space Forms ◽  
Lorentzian Space ◽  
Null Hypersurfaces ◽  
Shape Operators ◽  
Lorentzian Space Forms

We define two types of null hypersurfaces as; isoparametric and quasi isoparametric null hypersurfaces of Lorentzian space forms, based on the two shape operators associated with a null hypersurface. We prove that; on any screen conformal isoparametric null hypersurface, the screen geodesics lie on circles in the ambient space. Furthermore, we prove that the screen distributions of isoparametric (or quasi-parametric) null hypersurfaces with at most two principal curvatures are generally Riemannian products. Several examples are also given to illustrate the main concepts.

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