P. Wintgen proved in Sur l'inégalité de Chen-Willmore. CR Acad. Sci. Paris 288, 993–995
(1979) that the Gauss curvature G and the normal curvature K^D of a surface in the …

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 …

The study of warped products plays versatile roles in differential geometry as well as in
mathematical physics, especially in general relativity (GR). In the present paper, we study …

Chen inequalities for statistical submersions between statistical manifolds Page 1 International
Journal of Geometric Methods in Modern Physics Vol. 18, No. 4 (2021) 2150049 (17 pages) c© …

Mathematics | Free Full-Text | Chen Inequalities for Statistical Submanifolds of Kähler-Like
Statistical Manifolds Next Article in Journal Local Convergence and Attraction Basins of Higher …

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 …

Mathematics | Free Full-Text | Relations between Extrinsic and Intrinsic Invariants of Statistical
Submanifolds in Sasaki-Like Statistical Manifolds Next Article in Journal Generalization of the …

One of the most fundamental interests in submanifold theory is to establish simple
relationships between the main extrinsic invariants and the main intrinsic invariants of …

In this paper, we prove some inequalities between intrinsic and extrinsic curvature
invariants, namely involving the Chen first invariant and the mean curvature of totally real …

For submanifolds of general dimension and codimension in statistical manifolds of constant
curvature, a sharp inequality of Wintgen type is given by us. It generalizes the inequality …