*Department of Mathematics, University of Allahabad, Allahabad-211002, India
E-mail: ssshukla_au@rediffmail.com*and sanjaitiwarikt@rediffmail.com**
ABSTRACT
B.Y. Chen (1999) established a clear relationship involving intrinsic invariants, namely the sectional curvature and the scalar curvature and the main extrinsic invariants, namely the squared mean curvature for a submanifold in real space form with arbitrary co-dimension.
In this article, we establish inequalities between the Ricci curvature and the squared mean curvature, and also between the s-Ricci curvature and the scalar curvature for a slant, semi-slant and bi-slant submanifolds in (k,\mu )-contact space forms.
Mathematics Subject Classification (2000). 53C40.
Key words and phrases. Mean curvature, sectional curvature, scalar curvature, s-Ricci curvature, slant submanifold, semi-slant submanifold, bi-slant submanifold, (k,\mu )-contact space form.