B.Y. Chen inequalities for slant submanifolds in Sasakian space forms

2003 ◽  
Vol 52 (3) ◽  
pp. 367-381 ◽  
Author(s):  
Dragoş Cioroboiu ◽  
Adela Oiagă
Keyword(s):  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms

scholarly journals The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1151 ◽  
Author(s):  
Mohd. Aquib ◽  
Michel Nguiffo Boyom ◽  
Mohammad Hasan Shahid ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Fundamental Equation ◽  
Type Inequality ◽  
Lagrangian Submanifold ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Generalized Complex ◽  
Complex Space Forms

In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and generalized Sasakian space forms and derive some applications in various slant cases. Finally, we obtain obstructions to the existence of non-flat generalized complex space forms and non-flat generalized Sasakian space forms in terms of dimension of the vector space of solutions to the first fundamental equation on such spaces.

scholarly journals Characterizing Inequalities for Biwarped Product Submanifolds of Sasakian Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Meraj Ali Khan ◽  
Ibrahim Al-dayel
Keyword(s):  
Fundamental Form ◽  
Warped Product ◽  
Second Fundamental Form ◽  
Space Forms ◽  
Slant Submanifolds ◽  
The Second Fundamental Form ◽  
Sasakian Space Forms

The biwarped product submanifolds generalize the class of product submanifolds and are particular case of multiply warped product submanifolds. The present paper studies the biwarped product submanifolds of the type S T × ψ 1 S ⊥ × ψ 2 S θ in Sasakian space forms S ¯ c , where S T , S ⊥ , and S θ are the invariant, anti-invariant, and pointwise slant submanifolds of S ¯ c . Some characterizing inequalities for the existence of such type of submanifolds are proved; besides these inequalities, we also estimated the norm of the second fundamental form.

scholarly journals On 3-dimensional contact slant submanifolds in Sasakian space forms

2003 ◽  
Vol 68 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Ion Mihai ◽  
Yoshihiko Tazawa
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Sharp Inequality ◽  
Sasakian Space Form ◽  
Slant Submanifold ◽  
Space Forms ◽  
3 Dimensional ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Complex Space Forms

Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot be minimal.

A New Class of Slant Submanifolds in Generalized Sasakian Space Forms

2020 ◽  
Vol 17 (3) ◽  
Author(s):  
Pablo Alegre ◽  
Joaquín Barrera ◽  
Alfonso Carriazo
Keyword(s):  
Space Forms ◽  
New Class ◽  
Slant Submanifolds ◽  
Sasakian Space Forms

scholarly journals Optimal casorati inequalities on bi-slant submanifolds of generalized sasakian space forms

2018 ◽  
Vol 49 (3) ◽  
pp. 235-255 ◽  
Author(s):  
Aliya Naaz Siddiqui
Keyword(s):  
Scalar Curvature ◽  
Optimization Method ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Normalized Scalar Curvature

In this paper, we use T Oprea's optimization method to establish some optimal Casorati inequalities, which involve the normalized scalar curvature for bi-slant submanifolds of generalized Sasakian space forms. In the continuation, we show that in both cases, the equalities hold if and only if submanifolds are invariantly quasi-umbilical.

scholarly journals Some Eigenvalues Estimate for the ϕ -Laplace Operator on Slant Submanifolds of Sasakian Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yanlin Li ◽  
Akram Ali ◽  
Fatemah Mofarreh ◽  
Abimbola Abolarinwa ◽  
Rifaqat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Space Form ◽  
Upper Bounds ◽  
Laplacian Operator ◽  
First Eigenvalue ◽  
Sasakian Space Form ◽  
Slant Submanifold ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms

This paper is aimed at establishing new upper bounds for the first positive eigenvalue of the ϕ -Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the ϕ -Laplacian operator on closed oriented m -dimensional slant submanifolds in a Sasakian space form M ~ 2 k + 1 ε is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the ϕ -Laplacian on slant submanifold in a sphere S 2 n + 1 with ε = 1 and ϕ = 2 .

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