On Finsler Warped Product Metrics with Special Curvatures Properties

2022 ◽  
Author(s):  
Mehran Gabrani ◽  
Bahman Rezaei ◽  
Esra Sengelen Sevim
Keyword(s):  
Warped Product ◽  
Product Metrics

Finsler Warped Product Metrics of Douglas Type

2019 ◽  
Vol 62 (1) ◽  
pp. 119-130 ◽  
Author(s):  
Huaifu Liu ◽  
Xiaohuan Mo
Keyword(s):  
Differential Equation ◽  
Warped Product ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Product Metrics ◽  
Douglas Curvature

AbstractIn this paper, we study the warped structures of Finsler metrics. We obtain the differential equation that characterizes Finsler warped product metrics with vanishing Douglas curvature. By solving this equation, we obtain all Finsler warped product Douglas metrics. Some new Douglas Finsler metrics of this type are produced by using known spherically symmetric Douglas metrics.

scholarly journals Ricci flow with hyperbolic warped product metrics

2011 ◽  
Vol 284 (5-6) ◽  
pp. 739-746 ◽  
Author(s):  
Li Ma ◽  
Xingwang Xu
Keyword(s):  
Ricci Flow ◽  
Warped Product ◽  
Product Metrics

Warped Product Metrics with Rank-1 Ricci Tensor

2008 ◽  
Vol 30 ◽  
pp. 329-332
Author(s):  
A.H. Bilge ◽  
D. Daghan
Keyword(s):  
Ricci Tensor ◽  
Warped Product ◽  
Product Metrics

scholarly journals ON WARPED PRODUCT MANIFOLDS - CONFORMAL FLATNESS AND CONSTANT SCALAR CURVATURE PROBLEM

1998 ◽  
Vol 29 (3) ◽  
pp. 203-221
Author(s):  
KWANG-WU YANG
Keyword(s):  
Warped Product ◽  
Necessary Conditions ◽  
Constant Scalar Curvature ◽  
Topological Product ◽  
Product Manifold ◽  
Product Metrics ◽  
Conformal Flatness ◽  
Sufficient And Necessary Conditions ◽  
Linear Differential ◽  
Curvature Problem

In this paper, we study some geometric properties on doubly or singly warped­ product manifolds. In general, on a fixed topological product manifold, the problem for finding warped-product metrics satisfying certain curvature conditions are finally reduced to find positive solutions of linear or non-linear differential equations. Here, we are mainly interested in the following problems on essentially warped-product manifolds: one is the sufficient and necessary conditions for conformal flatness, and the other is to find warped-product metrics so that their scalar curvatures are contants.

Finsler warped product metrics with almost vanishing H-curvature

2020 ◽  
Vol 17 (12) ◽  
pp. 2050188
Author(s):  
Hongmei Zhu
Keyword(s):  
Warped Product ◽  
Product Metrics

In this paper, we show that a Finsler warped product metric is of almost vanishing [Formula: see text]-curvature if and only if it is of almost vanishing [Formula: see text]-curvature. Furthermore, the corresponding one form is exact.

scholarly journals Multiply-warped product metrics and reduction of Einstein equations

2017 ◽  
Vol 14 (02) ◽  
pp. 1750021 ◽  
Author(s):  
Fateme Gholami ◽  
Farhad Darabi ◽  
Ali Haji-Badali
Keyword(s):  
Cosmological Constant ◽  
Warped Product ◽  
Einstein Equations ◽  
Product Form ◽  
Product Metrics ◽  
Cosmological Constants

It is shown that for every multidimensional metric in the multiply-warped product form [Formula: see text] with warp functions [Formula: see text], [Formula: see text], associated to the submanifolds [Formula: see text], [Formula: see text] of dimensions [Formula: see text], [Formula: see text] respectively, one can find the corresponding Einstein equations [Formula: see text], with cosmological constant [Formula: see text], which are reducible to the Einstein equations [Formula: see text] and [Formula: see text] on the submanifolds [Formula: see text], [Formula: see text], with cosmological constants [Formula: see text] and [Formula: see text], respectively, where [Formula: see text], [Formula: see text] and [Formula: see text] are functions of [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text].

scholarly journals On Projectively Flat Finsler Warped Product Metrics of Constant Flag Curvature

2021 ◽  
Author(s):  
Huaifu Liu ◽  
Xiaohuan Mo
Keyword(s):  
Warped Product ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Product Metrics ◽  
Constant Flag Curvature ◽  
Projectively Flat ◽  
Spherically Symmetric Metric

AbstractIn this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these metrics by warped product. Using the obtained equations, we manufacture new locally projectively flat Finsler warped product metrics of vanishing flag curvature. These metrics contain the metric introduced by Berwald and the spherically symmetric metric given by Mo-Zhu.

scholarly journals Global isometric embeddings of multiple warped product metrics into quadrics

2015 ◽  
Vol 38 (1) ◽  
pp. 119-134 ◽  
Author(s):  
Heudson Mirandola ◽  
Feliciano Vitório
Keyword(s):  
Warped Product ◽  
Product Metrics ◽  
Isometric Embeddings
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