scholarly journals On conformally doubly warped product Finsler manifold

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
A. Soleiman ◽  
A.M. Abdelsalam
Keyword(s):  
Curvature Tensor ◽  
Warped Product ◽  
Finsler Manifold ◽  
Finsler Spaces ◽  
Barthel Connection

AbstractThe aim of the present paper is to introduce the notion of conformally doubly warped product Finsler manifold (CDWPF). For such a Finsler manifold, the coefficients of Barthel connection and its curvature tensor are investigated. The coefficients of Cartan, Berwald, Hashiguchi and Chern (Rund) connections of CDWPF are calculated. Some special Finsler spaces are studied.

On warped product Finsler spaces of Landsberg type

2011 ◽  
Vol 52 (9) ◽  
pp. 093506 ◽  
Author(s):  
Ataabak B. Hushmandi ◽  
Morteza M. Rezaii
Keyword(s):  
Warped Product ◽  
Finsler Spaces

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.

Geodesic orbit Finsler spaces with K ≥ 0 and the (FP) condition

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ming Xu
Keyword(s):  
Lie Algebra ◽  
Finsler Space ◽  
Finsler Manifold ◽  
Constant Speed ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Coset Space ◽  
Finsler Spaces ◽  
Negatively Curved ◽  
Positively Curved

Abstract We study the interaction between the g.o. property and certain flag curvature conditions. A Finsler manifold is called g.o. if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also consider the condition (FP) for the flag curvature, i.e. in any flag we find a flag pole such that the flag curvature is positive. By our main theorem, if a g.o. Finsler space (M, F) has non-negative flag curvature and satisfies (FP), then M is compact. If M = G/H where G has a compact Lie algebra, then the rank inequality rk 𝔤 ≤ rk 𝔥+1 holds. As an application,we prove that any even-dimensional g.o. Finsler space which has non-negative flag curvature and satisfies (FP) is a smooth coset space admitting a positively curved homogeneous Riemannian or Finsler metric.

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.

Recurrent Finsler manifolds under projective change

2016 ◽  
Vol 13 (10) ◽  
pp. 1650126 ◽  
Author(s):  
Amr Soleiman
Keyword(s):  
Curvature Tensor ◽  
Finsler Spaces ◽  
Finsler Manifolds ◽  
Projective Change ◽  
Douglas Tensor

The aim of the present paper is to provide an intrinsic investigation of some important special Finsler spaces. These spaces are related to the Berwald [Formula: see text]-curvature tensor of transformed manifold, the Douglas tensor and the projective deviation tensor of projective change. Three spaces are studied and called symmetric, [Formula: see text]-recurrent and [Formula: see text]-recurrent manifolds.

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].

scholarly journals Algebraicity of Induced Riemannian Curvature Tensor on Lightlike Warped Product Manifolds

2019 ◽  
Vol 07 (12) ◽  
pp. 3132-3139
Author(s):  
Domitien Ndayirukiye ◽  
Gilbert Nibaruta ◽  
Ménédore Karimumuryango ◽  
Aboubacar Nibirantiza
Keyword(s):  
Curvature Tensor ◽  
Warped Product ◽  
Riemannian Curvature ◽  
Riemannian Curvature Tensor
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