Geometry of Submanifolds of Almost r-paracontact Riemannian Manifold

The present text, Submanifolds of Almost r-paracontact Manifold, deals with the study of hypersurfaces and submanifolds of almost r-paracontact Riemannian manifold with certain connections. The semi-symmetric and quarter symmetric connections of non-metric, metric and semi-metric nature with respect to the Riemannian metric play very important role in study of hypersurfaces and submanifolds due to fact that the induced connection on submanifolds and hypersurfaces is of the same type as the connection of the ambient manifold. The characteristic properties of invariant, non-invariant, anti-invariant, totally geodesic and totally umbilical hypersurfaces are discussed and Gauss equation, Weingarten equation and curvature tensor of hypersurfaces and submanifolds are obtained for such connections.

Autorentext

Dr. Mobin Ahmad is an Associate Professor of Mathematics at Integral University India. He visited Jazan University at Saudi Arabia and worked as Associate Prof. for three years there. He published 03 books and 66 research papers in national and international journals of repute. 08 research scholars are awarded Ph. D. degree under his supervision.