scholarly journals On a non flat Riemannian warped product manifold with respect to quarter-symmetric connection

2019 ◽  
Vol 11 (2) ◽  
pp. 332-349
Author(s):  
Buddhadev Pal ◽  
Santu Dey ◽  
Sampa Pahan
Keyword(s):  
Warped Product ◽  
Einstein Manifold ◽  
Warped Products ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Symmetric Connection

Abstract In this paper, we study generalized quasi-Einstein warped products with respect to quarter symmetric connection for dimension n ≥ 3 and Ricci-symmetric generalized quasi-Einstein manifold with quarter symmetric connection. We also investigate that in what conditions the generalized quasi-Einstein manifold to be nearly Einstein manifold with respect to quarter symmetric connection. Example of warped product on generalized quasi-Einstein manifold with respect to quarter symmetric connection are also discussed.

scholarly journals On warped product manifolds satisfying Ricci-Hessian class type equations

2018 ◽  
Vol 103 (117) ◽  
pp. 69-75 ◽  
Author(s):  
Sinem Güler ◽  
Altay Demirbağ
Keyword(s):  
Smooth Function ◽  
Ricci Tensor ◽  
Warped Product ◽  
Einstein Manifold ◽  
Warped Products ◽  
Product Manifold ◽  
Warped Product Manifold

We deal with a study of warped product manifold which is also a generalized quasi Einstein manifold. Then, we investigate the relationships between such warped products and certain manifolds that provide some Ricci-Hessian type equations, such as Ricmf = ?g for some smooth function ?, where Ricmf denotes the m-Bakery-Emery Ricci tensor. Finally, we obtain some rigidity conditions for such manifolds.

scholarly journals Gradient almost Ricci solitons on multiply warped product manifolds

2021 ◽  
Vol 13 (2) ◽  
pp. 386-394
Author(s):  
S. Günsen ◽  
L. Onat
Keyword(s):  
Potential Field ◽  
Warped Product ◽  
Einstein Manifold ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Product Manifold ◽  
Rigidity Result ◽  
Warped Product Manifold ◽  
Almost Ricci Soliton

In this paper, we investigate multiply warped product manifold \[M =B\times_{b_1} F_1\times_{b_2} F_2\times_{b_3} \ldots \times_{b_m} F_m\] as a gradient almost Ricci soliton. Taking $b_i=b$ for $1\leq i \leq m$ lets us to deduce that potential field depends on $B$. With this idea we also get a rigidity result and show that base is a generalized quasi-Einstein manifold if $\nabla b$ is conformal.

scholarly journals A Study of Generalized Projective P − Curvature Tensor on Warped Product Manifolds

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Uday Chand De ◽  
Abdallah Abdelhameed Syied ◽  
Nasser Bin Turki ◽  
Suliman Alsaeed
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Warped Product ◽  
Einstein Manifold ◽  
Constant Scalar Curvature ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Divergence Free

The main aim of this study is to investigate the effects of the P − curvature flatness, P − divergence-free characteristic, and P − symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P − curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P − curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P − divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P − symmetric warped product manifold is considered.

Exit radii of submanifolds from cylindrical domains in warped product manifolds

2015 ◽  
Vol 145 (3) ◽  
pp. 559-569
Author(s):  
Hironori Kumura
Keyword(s):  
Lower Bound ◽  
Bounded Domain ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Cylindrical Domains ◽  
The Mean

Let UB(p0; ρ1) × f MV be a cylindrically bounded domain in a warped product manifold := MB × fMV and let M be an isometrically immersed submanifold in . The purpose of this paper is to provide explicit radii of the geodesic balls of M which first exit from UB(p0; ρ1) × fMV for the case in which the mean curvature of M is sufficiently small and the lower bound of the Ricci curvature of M does not diverge to –∞ too rapidly at infinity.

scholarly journals The W2-curvature tensor on warped product manifolds and applications

2016 ◽  
Vol 13 (07) ◽  
pp. 1650099 ◽  
Author(s):  
Sameh Shenawy ◽  
Bülent Ünal
Keyword(s):  
Curvature Tensor ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Static Space

The purpose of this paper is to study the [Formula: see text]-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson–Walker and standard static space-times. Some different expressions of the [Formula: see text]-curvature tensor on a warped product manifold in terms of its relation with [Formula: see text]-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate [Formula: see text]-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a [Formula: see text]-curvature flat warped product manifold are derived. Finally, we study the [Formula: see text]-curvature tensor on generalized Robertson–Walker and standard static space-times; we explore the geometry of the fiber of these warped product space-time models that are [Formula: see text]-curvature flat.

scholarly journals On some classes of mixed-super quasi-Einstein manifolds

2016 ◽  
Vol 8 (1) ◽  
pp. 32-52
Author(s):  
Santu Dey ◽  
Buddhadev Pal ◽  
Arindam Bhattacharyya
Keyword(s):  
Warped Product ◽  
Einstein Manifold ◽  
Warped Products ◽  
Einstein Manifolds

Abstract Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

scholarly journals A note on Weingarten hypersurfaces in the warped product manifold

2014 ◽  
Vol 25 (14) ◽  
pp. 1450121 ◽  
Author(s):  
Haizhong Li ◽  
Yong Wei ◽  
Changwei Xiong
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
Higher Order ◽  
Product Manifold ◽  
Weingarten Surfaces ◽  
Warped Product Manifold ◽  
Higher Order Mean Curvature ◽  
Special Case ◽  
Differential Geom

In this paper, we consider the closed embedded hypersurface Σ in the warped product manifold [Formula: see text] equipped with the metric g = dr2 + λ(r)2 gN. We give some characterizations of slice {r} × N by the condition that Σ has constant weighted higher-order mean curvatures (λ′)αpk, or constant weighted higher-order mean curvature ratio (λ′)αpk/p1, which generalize Brendle's [Constant mean curvature surfaces in warped product manifolds, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 247–269] and Brendle–Eichmair's [Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94(3) (2013) 387–407] results. In particular, we show that the assumption convex of Brendle–Eichmair's result [Isoperimetric and Weingarten surfaces in the Schwarzschild manifold, J. Differential Geom. 94(3) (2013) 387–407] is unnecessary. Here pk is the kth normalized mean curvature of the hypersurface Σ. As a special case, we also give some characterizations of geodesic spheres in ℝn, ℍn and [Formula: see text], which generalize the classical Alexandrov-type results.

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