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.

scholarly journals Inequality for Ricci curvature of certain submanifolds in locally conformal almost cosymplectic manifolds

2005 ◽  
Vol 2005 (10) ◽  
pp. 1621-1632 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Slant Submanifold ◽  
Cosymplectic Manifold ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Arbitrary Codimension ◽  
Locally Conformal

We establish inequalities between the Ricci curvature and the squared mean curvature, and also between thek-Ricci curvature and the scalar curvature for a slant, semi-slant, and bi-slant submanifold in a locally conformal almost cosymplectic manifold with arbitrary codimension.

scholarly journals Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product

2015 ◽  
Vol 23 (2) ◽  
pp. 259-277
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Curvature Tensor ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
Comparison Inequality

Abstract In this paper, by supposing a natural comparison inequality on the positive r-th mean curvatures of the hypersurface, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces immersed in a semi-Riemannian warped product of constant sectional curvature. Generalizing the above results, under a restriction on the sectional curvature or the Ricci curvature tensor of the fiber of a warped product, we also prove some new rigidity theorems in semi-Riemannian warped products. Our main results extend some recent Bernstein-type theorems proved in [12, 13, 14].

Some geometric obstructions to warped product immersions in locally conformal Kaehler space forms

2021 ◽  
pp. 2150181
Author(s):  
Mohd Hasan Shahid ◽  
Mohammed Aslam ◽  
Siraj Uddin
Keyword(s):  
Warped Product ◽  
Embedding Theorem ◽  
Warped Products ◽  
Space Forms ◽  
Equality Case ◽  
Locally Conformal ◽  
The Relationship

Being motivated by a well-known Nash’s embedding theorem, Chen introduced a method to discover the relationship for the extrinsic invariants controlled by the intrinsic one. In this paper, we extend Chen’s inequality for the intrinsic and extrinsic invariants for pointwise bi-slant warped products in locally conformal Kaehler space forms with quarter-symmetric and semi-symmetric connections. The equality case of the inequality is also investigated. Several applications of the inequality are given. Furthermore, we provide two non-trivial examples of such immersions.

scholarly journals Geometric inequalities for CR-warped product submanifolds of locally conformal almost cosymplectic manifolds

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 741-748
Author(s):  
Akram Ali ◽  
Wan Othman ◽  
Sayyadah Qasem
Keyword(s):  
Sectional Curvature ◽  
Fundamental Form ◽  
Warped Product ◽  
Second Fundamental Form ◽  
Integration Theory ◽  
Warping Function ◽  
Geometric Inequalities ◽  
The Second Fundamental Form ◽  
Cosymplectic Manifolds ◽  
Locally Conformal

In this paper, we establish some inequalities for the squared norm of the second fundamental form and the warping function of warped product submanifolds in locally conformal almost cosymplectic manifolds with pointwise ?-sectional curvature. The equality cases are also considered. Moreover, we prove a triviality result for CR-warped product submanifold by using the integration theory on a compact orientate manifold without boundary.

scholarly journals Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 797 ◽  
Author(s):  
Aliya Siddiqui ◽  
Bang-Yen Chen ◽  
Oğuzhan Bahadır
Keyword(s):  
Differential Geometry ◽  
Scalar Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Mathematical Physics ◽  
Warping Function ◽  
Warped Products ◽  
Statistical Manifold ◽  
Statistical Manifolds ◽  
Levi Civita Connection

Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products R × f N 2 and N 1 × f R . Second, we study statistical warped products as submanifolds of statistical manifolds. For statistical warped products statistically immersed in a statistical manifold of constant curvature, we prove Chen’s inequality involving scalar curvature, the squared mean curvature, and the Laplacian of warping function (with respect to the Levi–Civita connection). At the end, we establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds in the same ambient space.

scholarly journals CONSTANT MEAN CURVATURE HYPERSURFACES IN WARPED PRODUCT SPACES

2007 ◽  
Vol 50 (3) ◽  
pp. 511-526 ◽  
Author(s):  
Luis J. Alías ◽  
Marcos Dajczer
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
Complete Riemannian Manifold ◽  
General Situation ◽  
Warped Products ◽  
General Version ◽  
Product Spaces ◽  
Constant Mean Curvature Hypersurfaces ◽  
Warped Product Spaces

AbstractWe study hypersurfaces of constant mean curvature immersed into warped product spaces of the form $\mathbb{R}\times_\varrho\mathbb{P}^n$, where $\mathbb{P}^n$ is a complete Riemannian manifold. In particular, our study includes that of constant mean curvature hypersurfaces in product ambient spaces, which have recently been extensively studied. It also includes constant mean curvature hypersurfaces in the so-called pseudo-hyperbolic spaces. If the hypersurface is compact, we show that the immersion must be a leaf of the trivial totally umbilical foliation $t\in\mathbb{R}\mapsto\{t\}\times\mathbb{P}^n$, generalizing previous results by Montiel. We also extend a result of Guan and Spruck from hyperbolic ambient space to the general situation of warped products. This extension allows us to give a slightly more general version of a result by Montiel and to derive height estimates for compact constant mean curvature hypersurfaces with boundary in a leaf.

scholarly journals Chen’s improved inequality for pointwise hemi-slant warped products in Kaehler manifolds

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 807-814
Author(s):  
Monia Naghi ◽  
Mica Stankovic ◽  
Fatimah Alghamdi
Keyword(s):  
Fundamental Form ◽  
Warped Product ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Warped Products ◽  
Equality Case ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
The Second Fundamental Form

Recently, B.-Y. Chen discovered a technique to find the relation between second fundamental form and the warping function of warped product submanifolds. In this paper, we extend our further study of [24] by giving non-trivial examples of warped product pointwise hemi-slant submanifolds. Finally, we establish a sharp estimation for the squared norm of the second fundamental form ||h||2 in terms of the warping function f. The equality case is also investigated.

scholarly journals A note on warped product submanifolds of cosymplectic manifolds

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 95-102 ◽  
Author(s):  
Siraj Uddin ◽  
V.A. Khan ◽  
K.A. Khan
Keyword(s):  
Warped Product ◽  
Warped Products ◽  
Cosymplectic Manifold ◽  
Slant Submanifolds ◽  
Cosymplectic Manifolds

In this paper, we study warped product anti-slant submanifolds of cosymplectic manifolds. It is shown that the cosymplectic manifold do not admit non trivial warped product submanifolds in the form N??f N? and then we obtain some results for the existence of warped products of the type N??f N?, where N? and N? are anti-invariant and proper slant submanifolds of a cosymplectic manifold M?, respectively.

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.

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