Geometry of Submanifolds of Almost r-paracontact Riemannian Manifold

The book "Geometry of Submanifolds of Almost r-paracontact Riemannian Manifold" offers a comprehensive examination of hypersurfaces and submanifolds within the framework of almost r-paracontact Riemannian manifolds. It highlights the role of semi-symmetric and quarter-symmetric connections, which exhibit both non-metric and metric properties. These connections are crucial for understanding the induced connections on submanifolds and hypersurfaces, as they share the same properties as the connections of the surrounding manifold. The work addresses the characteristic properties of invariant, non-invariant, anti-invariant, totally geodesic, and totally umbilical hypersurfaces. Additionally, the Gauss equation, the Weingarten equation, and the curvature tensor for hypersurfaces and submanifolds are derived in this specific context.