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].

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.

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’.

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.

scholarly journals Kinematic formula and tube formula in space of constant curvature

1990 ◽  
Vol 33 (1) ◽  
pp. 79-88
Author(s):  
Sungyun Lee
Keyword(s):  
Euclidean Space ◽  
Euler Characteristic ◽  
Constant Curvature ◽  
Kinematic Formula ◽  
Curvature Invariants ◽  
Space Of Constant Curvature

The Euler characteristic of an even dimensional submanifold in a space of constant curvature is given in terms of Weyl's curvature invariants. A derivation of Chern's kinematic formula in non-Euclidean space is completed. As an application of above results Weyl's tube formula about an odd-dimensional submanifold in a space of constant curvature is obtained.

Simplexes in spaces of constant curvature

1991 ◽  
Vol 38 (1) ◽  
Author(s):  
B.V. Dekster ◽  
J.B. Wilker
Keyword(s):  
Constant Curvature ◽  
Spaces Of Constant Curvature
Sign in / Sign up

Export Citation Format

Share Document