A Study of Distributions £ and ℳ of Generalized Kenmotsu Manifold
C. S. Bagewadi
Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, India.
S. Venkatesha *
Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, India.
*Author to whom correspondence should be addressed.
Abstract
The object of the present paper is to study the geometry of distributions £ and ℳ of the generalized Kenmotsu manifold. Using the totally umbilicity of the distributions £ and ℳ, it is shown that if M is totally umbilical then it is totally geodesic. Also, the integrability of the distributions £ and M are proved. Further geometric conditions connecting the distribution ℳ and submanifold M are obtained.
Keywords: Geometry of submanifold, Generalized Kenmotsu manifold, M- totally umbilical and M-totally geodesic, £-totally umbilical and £-totally geodesic, integrability of the distributions.