The first part of this book provides a self-contained and accessible introduction to the subject
in the general setting of pseudo-Riemannian manifolds and their non-degenerate …

The famous Nash embedding theorem was aimed for in the hope that if Riemannian
manifolds could be regarded as Riemannian submanifolds, this would then yield the …

In this article, we derive Chen's inequalities involving Chen's δ-invariant δ M, Riemannian
invariant δ (m 1,⋯, mk), Ricci curvature, Riemannian invariant Θ k (2≤ k≤ m), the scalar …

CHEN’S INEQUALITIES FOR SUBMANIFOLDS OF A RIEMANNIAN MANIFOLD OF QUASI-CONSTANT
CURVATURE WITH A SEMI-SYMMETRIC METRIC CONNECT Page 1 TAIWANESE …

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 …

We introduce k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a
Lorentzian manifold. We establish some inequalities between the extrinsic scalar curvature …

The Casorati curvature of a submanifold M< sup> n of a Riemannian manifold M~< sup> n+
m is known to be the normalized square of the length of the second fundamental form, C …

In this paper, we establish some inequalities involving k-Ricci curvature, k-scalar curvature,
the screen scalar curvature on a screen homothetic lightlike hypersurface of a Lorentzian …

In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and
the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a …

We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the
hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared …