Abstract The theory of $\delta $-invariants, initiated by the author in the early 1990s, is a
challenging topic in modern differential geometry, having a lot of applications. In the spirit of …

In this paper, we establish two sharp inequalities for the normalized δ-Casorati curvatures of
submanifolds in a Kenmotsu space form, tangent to the structure vector field of the ambient …

The notion of different kind of algebraic Casorati curvatures are introduced. Some results
expressing basic Casorati inequalities for algebraic Casorati curvatures are presented …

Warped products play crucial roles in differential geometry, as well as in mathematical
physics, especially in general relativity. In this article, first we define and study statistical …

In 2017, CW Lee et al. derived optimal Casorati inequalities with normalized scalar
curvature for statistical submanifolds of statistical manifolds of constant curvature. In this …

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian
manifolds or (α, β)-type almost contact manifolds endowed with the Schouten–Van Kampen …

A pinching theorem for statistical manifolds with Casorati curvatures Page 1 Available online at
www.isr-publications.com/jnsa J. Nonlinear Sci. Appl., 10 (2017), 4908–4914 Research Article …

This research deals with the generalized symmetric metric U-connection defined on golden
Lorentzian manifolds. We also derive sharp geometric inequalities that involve generalized …

In the present paper, we derive optimal inequalities involving generalized normalized δ δ-
Casorati curvatures for slant submanifolds in a golden Riemannian space form. We obtain …

By using new algebraic techniques, two Casorati inequalities are established for
submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric …