Abstract
An optimal inequality involving the scalar curvatures, the mean curvature and the k-Chen invariant is established for Riemannian submanifolds. Particular cases of this inequality is reported. Furthermore, this inequality is investigated on submanifolds, namely slant, F-invariant and F-anti invariant submanifolds of an almost constant curvature manifold.
Highlights
An optimal inequality involving the scalar curvatures, the mean curvature and the k-Chen invariant is established for Riemannian submanifolds
Particular cases of this inequality is reported. This inequality is investigated on submanifolds, namely slant, F -invariant and F -anti invariant submanifolds of an almost constant curvature manifold
Riemannian invariants have an essential role in Riemannian geometry since they a¤ect the intrinsic features of Riemannian manifolds
Summary
Riemannian invariants have an essential role in Riemannian geometry since they a¤ect the intrinsic features of Riemannian manifolds. In [8], he introduced and investigated two strings of new types of curvature invariants These new curvature invariants seem to play signi...cant roles in several areas of mathematics including submanifold theory and Riemannian, spectral and symplectic geometries. Proper slant surfaces of locally product Riemannian manifolds were investigated by the ...rst and third authors and S. Chen-Ricci inequalities for slant submanifolds of a Riemannian product manifold were established by the authors in [12]. Based on the above presented facts, we are going to give some relations involving the Chen invariants, the intrinsic and extrinsic curvature invariants of a Riemannian submanifold. We are going to investigate these relations on submanifolds of a Riemannian product manifold and an almost constant curvature manifold
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