Chen inequalities for submanifolds of a cosymplectic space form with a semi-symmetric metric connection

2012 ◽  
Vol 58 (2) ◽  
Author(s):  
Cihan Özgür ◽  
Cengizhan Murathan
Keyword(s):  
Space Form ◽  
Metric Connection

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.

scholarly journals Chen’s inequalities for submanifolds in (κ, μ)-contact space form with a semi-symmetric metric connection

2018 ◽  
Vol 16 (1) ◽  
pp. 380-391
Author(s):  
Asif Ahmad ◽  
He Guoqing ◽  
Tang Wanxiao ◽  
Zhao Peibiao
Keyword(s):  
Space Form ◽  
Metric Connection ◽  
Contact Space

AbstractIn this paper, we obtain Chen’s inequalities for submanifolds in (κ, μ)-contact space form endowed with a semi-symmetric metric connection.

scholarly journals Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ali H. Al-Khaldi ◽  
Mohd. Aquib ◽  
Mohd Aslam ◽  
Meraj Ali Khan
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Lagrangian Submanifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Generalized Complex ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Symmetric Connection ◽  
Legendrian Submanifold

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.

scholarly journals Inequalities on Generalized Sasakian Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Najma Abdul Rehman ◽  
Abdul Ghaffar ◽  
Esmaeil Abedi ◽  
Mustafa Inc ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Space Form ◽  
Variational Formula ◽  
Stability Criteria ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
The Stability ◽  
Second Variational Formula

In this paper, we find the second variational formula for a generalized Sasakian space form admitting a semisymmetric metric connection. Inequalities regarding the stability criteria of a compact generalized Sasakian space form admitting a semisymmetric metric connection are established.

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