A classification of totally umbilical proper slant and hemi-slant submanifolds of (k, μ)-contact manifolds

M S Siddesha; M M Praveena; C S Bagewadi

doi:10.56424/jts.v14i01.10608

M S Siddesha Department of Mathematics, Jain University, Bengaluru-562112, Karnataka, INDIA.
M M Praveena Department of Mathematics, M.S. Ramaiah Institute of Technology, Bangalore-54, Affiliated to VTU, Belagavi, Karnataka, INDIA.
C S Bagewadi Department of Mathematics, Kuvempu University, Shankaraghatta - 577 451, Shimoga, Karnataka, INDIA.

DOI: https://doi.org/10.56424/jts.v14i01.10608

Keywords: Slant submanifold, hemi-slant submanifold, totally umbilical, totally geodesic, (k, μ)-contact manifold.

Abstract

The object of the present paper is to study slant and hemi-slant submanifolds of (k, μ)- contact manifolds which are totally umbilical. We prove that every totally umbilical proper slant submanifold M of a (k, μ)-contact manifold ˜M is either totally geodesic or if M is not totally geodesic then we derive a formula for slant angle. Also necessary and sufficient conditions for distributions of hemi-slant submanifolds to be integrable are worked out. Further we give a characterization theorem.