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.

AN OPTIMAL INEQUALITY FOR CR-WARPED PRODUCTS IN COMPLEX SPACE FORMS INVOLVING CR δ-INVARIANT

2012 ◽  
Vol 23 (03) ◽  
pp. 1250045 ◽  
Author(s):  
BANG-YEN CHEN
Keyword(s):  
Euclidean Space ◽  
Warped Product ◽  
Complex Space ◽  
Warped Products ◽  
Space Forms ◽  
Equality Case ◽  
Complex Euclidean Space ◽  
Optimal Inequality ◽  
Complex Space Forms

We prove a new optimal inequality for CR-warped products in complex space forms involving a CR δ-invariant. Moreover, we completely classify CR-warped product submanifolds in complex Euclidean space which satisfy the equality case of the inequality.

scholarly journals Real hypersurfaces of indefinite Kaehler manifolds

1993 ◽  
Vol 16 (3) ◽  
pp. 545-556 ◽  
Author(s):  
A. Bejancu ◽  
K. L. Duggal
Keyword(s):  
Complex Space ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Sasakian Manifolds ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Almost Contact Metric ◽  
Metric Structures ◽  
Complex Space Forms ◽  
Almost Contact Metric Structures

We show the existence of ( ϵ )-almost contact metric structures and give examples of ( ϵ )-Sasakian manifolds. Then we get a classification theorem for real hypersurfaces of indefinite complex space-forms with parallel structure vector field. We prove that ( ϵ )-Sasakian real hypersurfaces of a semi-Euclidean space are either open sets of the pseudosphereS2S2n+1(1) or of the pseudohyperbolic spaceH2S−12n+1(1). Finally, we get the causal character of ( ϵ ) cosymplectic real hypersurfaccs of indefinite complex space-forms.

Sign in / Sign up

Export Citation Format

Share Document