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

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

Author

M.S. Siddesha,  M.M. Praveena  and C.S. Bagewadi

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.

2010 Mathematics Subject Classification: 53C42, 53C25, 53C40. Keywords: Slant submanifold, hemi-slant submanifold, totally umbilical, totally
geodesic, (k, μ)-contact manifold.

Received February 20, 2021
Accepted June 24, 2021
Published August 16, 2021

cited by : Journal of The Tensor Society (J.T.S.)  Vol. 14 (2020), page 30 – 39.