Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

Abstract

In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.

Inequalities for the Class of Warped Product Submanifold of Para-Cosymplectic Manifolds

“…Recently, there are many interesting papers related with submanifold theory, singularity theory, classical differential geometry, etc. The readers can find more details about those techniques and theories in a series of papers [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Moreover, interdisciplinary research is one of the hottest trends in science; in the future work, we intend to apply and combine the techniques and results presented in [16][17][18][19][20][21][22][23][24][25] alongside with the methods in this paper to obtain more new results.…”