Geometry of Submanifolds of Almost R-Paracontact Riemannian Manifold : A New Approach

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.