scholarly journals Some remarks on invariant lightlike submanifolds of indefinite Sasakian manifold

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Samuel Ssekajja
Keyword(s):  
Constant Curvature ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Spaces Of Constant Curvature ◽  
Content Type ◽  
Geometric Conditions ◽  
Reference Number ◽  
Space Of Constant Curvature ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

PurposeThe author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M′ of its screen distribution S(TM) are, also, spaces of constant curvature 1.Design/methodology/approachThe author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7.FindingsThe author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4).Originality/valueTo the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.

Integrable spreads and spaces of constant curvature

1988 ◽  
Vol 109 (3-4) ◽  
pp. 225-229 ◽  
Author(s):  
H. R. Farran ◽  
S. A. Robertson
Keyword(s):  
Vector Bundle ◽  
Vector Space ◽  
Constant Curvature ◽  
Affine Space ◽  
Sufficient Conditions ◽  
Spaces Of Constant Curvature ◽  
Space Of Constant Curvature

SynopsisThis paper is a continuation of [2], where we introduced the notion of global k-spreads on manifolds. Here we show that the space of all k-spreads on a manifold has the structure of an affine space, modelled on the vector space of sections of a certain vector bundle. We give some sufficient conditions for a manifold admitting an integrable k-spread to be a space of constant curvature and answer one of the questions raised in [2].

Some characterization theorems on holomorphic sectional curvature of GCR-lightlike submanifolds

2017 ◽  
Vol 14 (03) ◽  
pp. 1750034 ◽  
Author(s):  
Varun Jain ◽  
Rachna Rani ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sectional Curvature ◽  
Sasakian Manifold ◽  
Holomorphic Sectional Curvature ◽  
Bisectional Curvature ◽  
Holomorphic Bisectional Curvature ◽  
Characterization Theorems ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Sasakian manifold and obtain some characterization theorems on holomorphic sectional and holomorphic bisectional curvature.

An investigation on the existence of warped product irrotational screen-real lightlike submanifolds of metallic semi-Riemannian manifolds

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gauree Shanker ◽  
Ankit Yadav
Keyword(s):  
Riemannian Manifolds ◽  
Design Methodology ◽  
Warped Product ◽  
Sufficient Conditions ◽  
Totally Geodesic ◽  
Content Type ◽  
Lightlike Submanifolds ◽  
Totally Geodesic Foliation ◽  
Is Design ◽  
Lightlike Submanifold

PurposeThe purpose of this paper is to study the geometry of screen real lightlike submanifolds of metallic semi-Riemannian manifolds. Also, the authors investigate whether these submanifolds are warped product lightlike submanifolds or not.Design/methodology/approachThe paper is design as follows: In Section 3, the authors introduce screen-real lightlike submanifold of metallic semi Riemannian manifold. In Section 4, the sufficient conditions for the radical and screen distribution of screen-real lightlike submanifolds, to be integrable and to be have totally geodesic foliation, have been established. Furthermore, the authors investigate whether these submanifolds can be written in the form of warped product lightlike submanifolds or not.FindingsThe geometry of the screen-real lightlike submanifolds has been studied. Also various results have been established. It has been proved that there does not exist any class of irrotational screen-real r-lightlike submanifold such that it can be written in the form of warped product lightlike submanifolds.Originality/valueAll results are novel and contribute to further study on lightlike submanifolds of metallic semi-Riemannian manifolds.

scholarly journals On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Manish Gogna ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractAfter brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-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 Lambert's theorem and projective dynamics

2019 ◽  
Vol 377 (2158) ◽  
pp. 20180417
Author(s):  
Alain Albouy ◽  
Lei Zhao
Keyword(s):  
Constant Curvature ◽  
Vortex Dynamics ◽  
Kepler Problem ◽  
Keplerian Orbit ◽  
Theme Issue ◽  
Spaces Of Constant Curvature ◽  
Elapsed Time ◽  
Space Of Constant Curvature

We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We prove that the Hooke problem has a property similar to Lambert's theorem, which also extends to the spaces of constant curvature. This article is part of the theme issue ‘Topological and geometrical aspects of mass and vortex dynamics’.

scholarly journals A note on quasi-generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifolds

2017 ◽  
Vol 14 (03) ◽  
pp. 1750045
Author(s):  
Fortuné Massamba ◽  
Samuel Ssekajja
Keyword(s):  
Existence Theorem ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Metric Connection ◽  
Nearly Sasakian ◽  
Main Ideas ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

The concept of quasi-generalized CR-lightlike was first introduced by the authors in [Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds, Arab. J. Math. 5 (2016) 87–101]. In this paper, we focus on ascreen and co-screen quasi-generalized CR-lightlike submanifolds of indefinite nearly [Formula: see text]-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi-generalized CR-lightlike submanifolds admitting a metric connection. Classification theorems on nearly parallel and auto-parallel distributions on a co-screen quasi-generalized CR-lightlike submanifold are also given. Several examples are also constructed, where necessary, to illustrate the main ideas.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

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