Bulletin of the
Korean Mathematical Society BKMS

B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen \cite{DMV} established Chen first inequality for $C$-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo \cite{Car}. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

Keywords: Sasakian space forms, special contact slant submanifolds, Chen invariants

MSC numbers: 53C25, 53B21, 53C40