Abstract
Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature. The notion of a semislant submanifold of a Sasakian manifold was introduced by J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez (1999). In the present paper, we establish Chen inequalities for semislant submanifolds in Sasakian space forms by using subspaces orthogonal to the Reeb vector field ξ.
Highlights
Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature
The Riemannian invariants of a Riemannian manifold are the intrinsic characteristics of the Riemannian manifold
We recall a string of Riemannian invariants on a Riemannian manifold [5]
Summary
Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature. Let M be an n-dimensional submanifold of a Riemannian manifold M . En} an orthonormal basis of the tangent space TpM.
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