Optimal inequalities for the normalized δ-Casorati curvatures of submanifolds in Kenmotsu space forms

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Chul Woo Lee ◽  
Jae Won Lee ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Space Forms ◽  
Optimal Inequalities

AbstractIn this paper, we establish two sharp inequalities for the normalized

Certain inequalities for the Casorati curvatures of submanifolds of generalized (k,μ)-space-forms

2018 ◽  
Vol 13 (02) ◽  
pp. 2050040
Author(s):  
Shyamal Kumar Hui ◽  
Pradip Mandal ◽  
Ali H. Alkhaldi ◽  
Tanumoy Pal
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Space Forms ◽  
Civita Connection ◽  
Metric Connection ◽  
Levi Civita Connection ◽  
Casorati Curvature ◽  
Optimal Inequalities

The paper deals with the study of Casorati curvature of submanifolds of generalized [Formula: see text]-space-form with respect to Levi-Civita connection as well as semisymmetric metric connection and derived two optimal inequalities between scalar curvature and Casorati curvature of such space forms. The equality cases are also considered.

Optimal inequalities for contact CR-submanifolds in almost contact metric manifolds

2021 ◽  
Vol 71 (2) ◽  
pp. 513-521
Author(s):  
Andreea Olteanu
Keyword(s):  
Complex Space ◽  
Warped Products ◽  
Space Forms ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Optimal Inequality ◽  
Complex Space Forms ◽  
Almost Contact Metric Manifolds ◽  
Optimal Inequalities ◽  
Cr Submanifolds

Abstract In [An optimal inequality for CR-warped products in complex space forms involving CR δ-invariant, Internat. J. Math. 23(3) (2012)], B.-Y. Chen introduced the CR δ-invariant for CR-submanifolds. Then, in [Two optimal inequalities for anti-holomorphic submanifolds and their applications, Taiwan. J. Math. 18 (2014), 199–217], F. R. Al-Solamy, B.-Y. Chen and S. Deshmukh proved two optimal inequalities for anti-holomorphic submanifolds in complex space forms involving the CR δ-invariant. In this paper, we obtain optimal inequalities for this invariant for contact CR-submanifolds in almost contact metric manifolds.

scholarly journals A Riemannian invariant and its applications to Einstein manifolds

2004 ◽  
Vol 70 (1) ◽  
pp. 55-65 ◽  
Author(s):  
Bang-Yen Chen
Keyword(s):  
Mean Curvature ◽  
Real Space ◽  
Einstein Manifolds ◽  
Space Forms ◽  
Real Space Forms ◽  
Optimal Inequalities

We introduce a Riemannian invariant and establish general optimal inequalities involving the invariants and the squared mean curvature for Einstein manifolds isometrically immersed in real space forms. We show that these inequalities do not hold for arbitrary submanifolds in real space forms in general. We also provide some immediate applications of the inequalities.

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

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