scholarly journals Bounds for generalized normalized δ-Casorati curvatures for Bi-slant submanifolds in T-space forms

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 329-340 ◽  
Author(s):  
Mohd. Aquib
Keyword(s):  
Scalar Curvature ◽  
Space Forms ◽  
Equality Case ◽  
Slant Submanifolds ◽  
Invariant Submanifolds ◽  
Normalized Scalar Curvature ◽  
Cr Submanifolds

In this paper, we prove the inequality between the generalized normalized ?-Casorati curvatures and the normalized scalar curvature for the bi-slant submanifolds in T-space forms and consider the equality case of the inequality. We also develop same results for semi-slant submanifolds, hemi-slant submanifolds, CR-submanifolds, slant submanifolds, invariant and anti-invariant submanifolds in T-space forms.

Some inequalities of slant submanifolds in generalized complex space forms

2005 ◽  
Vol 36 (3) ◽  
pp. 223-229 ◽  
Author(s):  
Aimin Song ◽  
Ximin Liu
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Normalized Scalar Curvature

In this paper, we obtain an inequality about Ricci curvature and squared mean curvature of slant submanifolds in generalized complex space forms. We also obtain an inequality about the squared mean curvature and the normalized scalar curvature of slant submanifolds in generalized coplex 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 On the normal scalar curvature conjecture for legendrian submanifolds in Kenmotsu space forms

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3885-3891
Author(s):  
Monia Naghi ◽  
Mica Stankovic ◽  
Fatimah Alghamdi
Keyword(s):  
Scalar Curvature ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Legendrian Submanifolds

In this paper, we prove DDVV conjecture (the generalized Wintgen inequality) for Legendrian submanifolds in Kenmotsu space forms. Further, we derive an inequality for slant submanifolds in Kenmotsu space forms.

scholarly journals Three-dimensional CR-submanifolds in the nearly Kaehler six-sphere satisfying B.Y. Chen's basic equality

2000 ◽  
Vol 31 (4) ◽  
pp. 289-296
Author(s):  
Tooru Sasahara
Keyword(s):  
Mean Curvature ◽  
Three Dimensional ◽  
Real Space ◽  
Sharp Inequality ◽  
Space Forms ◽  
Equality Case ◽  
3 Dimensional ◽  
Real Space Forms ◽  
Basic Equality ◽  
Cr Submanifolds

B. Y. Chen introduced in [3] an important Riemannian invariant for a Riemannian manifold and obtained a sharp inequality between his invariant and the squared mean curvature for arbitrary submanifolds in real space forms. In this paper we investigate 3-dimensional CR-submanifolds in the nearly Kaehler 6-sphere which realize the equality case of the inequality.

A lower bound of normalized scalar curvature for the submanifolds of locally conformal Kaehler space form using Casorati curvatures

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4925-4932 ◽  
Author(s):  
Mehraj Lone
Keyword(s):  
Lower Bound ◽  
Scalar Curvature ◽  
Space Form ◽  
Equality Case ◽  
Locally Conformal ◽  
Normalized Scalar Curvature

In the present paper, we prove the inequality between the normalized scalar curvature and the generalized normalized ?-Casorati curvatures for the submanifolds of locally conformal Kaehler space form and also consider the equality case of the inequality.

Warped product pointwise semi-slant submanifolds of cosymplectic space forms and their applications

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lamia Saeed Alqahtani
Keyword(s):  
Warped Product ◽  
Sharp Estimate ◽  
Second Fundamental Form ◽  
Ricci Solitons ◽  
Warping Function ◽  
Dirichlet Energy ◽  
Space Forms ◽  
Equality Case ◽  
Slant Submanifolds ◽  
The Second Fundamental Form

In this paper some characterizations for the existence of warped product pointwise semi-slant submanifolds of cosymplectic space forms are obtained. Moreover, a sharp estimate for the squared norm of the second fundamental form is investigated, the equality case is also discussed. By the application of derived inequality, we compute an expression for Dirichlet energy of the involved warping function. Finally, we also proved some classifications for these warped product submanifolds in terms of Ricci solitons and Ricci curvature. A non-trivial example of these warped product submanifolds is provided.

scholarly journals CR-Submanifolds of Generalized -Space Forms

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Mahmood Jaafari Matehkolaee
Keyword(s):  
Scalar Curvature ◽  
Sectional Curvature ◽  
Upper Bound ◽  
Ricci Tensor ◽  
Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Cr Submanifold ◽  
Special Cases ◽  
Cr Submanifolds

We study sectional curvature, Ricci tensor, and scalar curvature of submanifolds of generalized -space forms. Then we give an upper bound for foliate -horizontal (and vertical) CR-submanifold of a generalized -space form and an upper bound for minimal -horizontal (and vertical) CR-submanifold of a generalized -space form. Finally, we give the same results for special cases of generalized -space forms such as -space forms, generalized Sasakian space forms, Sasakian space forms, Kenmotsu space forms, cosymplectic space forms, and almost -manifolds.

scholarly journals Improved Chen inequality of Sasakian space forms with the Tanaka-Webster connection

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1525-1533 ◽  
Author(s):  
Chul Lee ◽  
Jae Lee ◽  
Dae Yoon
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Space Forms ◽  
Equality Case ◽  
Sasakian Space Forms ◽  
Invariant Submanifolds ◽  
Chen Inequality

In this paper, we establish an improved Chen inequality between the pseudo-Ricci curvature and the square of pseudo mean curvature with respect to the Tanaka-Webster connection in Sasakian space forms, and also we study an improved Chen inequality for anti-invariant submanifolds. The equality case is considered.

scholarly journals A Closed Form for Slant Submanifolds of Generalized Sasakian Space Forms

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1238
Author(s):  
Pablo Alegre ◽  
Joaquín Barrera ◽  
Alfonso Carriazo
Keyword(s):  
Closed Form ◽  
Mean Curvature ◽  
Second Fundamental Form ◽  
Space Forms ◽  
Equality Case ◽  
Slant Submanifolds ◽  
The Second Fundamental Form ◽  
Sasakian Space Forms ◽  
Maslov Form ◽  
The Mean

The Maslov form is a closed form for a Lagrangian submanifold of C m , and it is a conformal form if and only if M satisfies the equality case of a natural inequality between the norm of the mean curvature and the scalar curvature, and it happens if and only if the second fundamental form satisfies a certain relation. In a previous paper we presented a natural inequality between the norm of the mean curvature and the scalar curvature of slant submanifolds of generalized Sasakian space forms, characterizing the equality case by certain expression of the second fundamental form. In this paper, first, we present an adapted form for slant submanifolds of a generalized Sasakian space form, similar to the Maslov form, that is always closed. And, in the equality case, we studied under which circumstances the given closed form is also conformal.

scholarly journals Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 259 ◽  
Author(s):  
Chul Lee ◽  
Jae Lee
Keyword(s):  
Scalar Curvature ◽  
Riemannian Metric ◽  
Statistical Manifold ◽  
Statistical Structure ◽  
Slant Submanifolds ◽  
Statistical Manifolds ◽  
Conjugate Connections ◽  
Levi Civita Connection ◽  
Normalized Scalar Curvature ◽  
Totally Real

A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and ∇ * in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C-totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant φ -sectional curvature. In addition, we give examples to show that the total space is a sphere.

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