Optimal Inequalities for Submanifolds in Trans-Sasakian Manifolds Endowed with a Semi-Symmetric Metric Connection

Abstract

In this paper, we improve the Chen first inequality for special contact slant submanifolds and Legendrian submanifolds, respectively, in (α,β) trans-Sasakian generalized Sasakian space forms endowed with a semi-symmetric metric connection.

Inequalities for the Generalized Normalized δ-Casorati Curvatures of Submanifolds in Golden Riemannian Manifolds

“…the inequality (14) or (15) obviously follows from (23). Additionally, the equality sign holds in (14) or (15) iff…”

“…In addition, the equality holds in ( 14) or (15) iff N satisfies the conditions discussed in Theorem 1 for the equality, and S r achieve the following forms:…”

“…Using the Chen invariants and the mean curvature, the primary extrinsic invariant for Riemannian submanifolds, he established sharp inequality relations that are known as Chen inequalities. Chen invariants and Chen inequalities for various submanifolds in different ambient spaces have been intensively investigated (see [10][11][12][13][14][15][16][17], etc. ).…”

Some Chen Inequalities for Submanifolds in Trans-Sasakian Manifolds Admitting a Semi-Symmetric Non-Metric Connection

“…In [18], we extended the definition of a special slant submanifold in a Sasakian manifold to trans-Sasakian manifolds.…”

“…In particular, the Chen δ-invariants for submanifolds of an ambient space admitting a semi-symmetric metric connection or a semi-symmetric non-metric connection have been discussed in [12][13][14][15][16][17][18].…”