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 …

One of the fundamental problems in the theory of submanifolds is to establish optimal
relationships between intrinsic and extrinsic invariants for submanifolds. In order to establish …

Riemannian maps are generalizations of well-known notions of isometric immersions and
Riemannian submersions. Most optimal inequalities on submanifolds in various ambient …

The purpose of this article is to establish some inequalities concerning the normalized δ-
Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of …

In this paper, we establish a new q-integral identity, the result is then used to derive two q-
integral inequalities of Simpson-type involving strongly preinvex functions. Some special …

The goal of this paper is to construct a fundamental theorem for the Ricci curvature
inequality via partially minimal isometric warped product immersions into an m-dimensional …

In the first part of this paper, using an optimization method on Riemannian submanifolds, we
prove that for any Legendrian submanifold of a Sasakian space form M ̄ 2 n+ 1 (c) of …

Curvature invariants of both intrinsic and extrinsic nature play a significant role in elucidating
the geometry of a spacetime. In particular, these invariants are useful in detecting event …

Chen inequalities for submanifolds of complex space forms and Sasakian space forms with
quarter-symmetric connections 1. Introdu Page 1 International Journal of Geometric …

Pointwise slant submanifolds were introduced by Chen and Garay (2012)[16] as a natural
generalization of slant submanifolds. On the other hand, pointwise slant submersions were …