scholarly journals On a class of Ricci-flat Finsler metrics in Finsler geometry

2013 ◽  
Vol 70 ◽  
pp. 30-38 ◽  
Author(s):  
Bin Chen ◽  
Zhongmin Shen ◽  
Lili Zhao
Keyword(s):  
Finsler Geometry ◽  
Finsler Metrics ◽  
Ricci Flat

Projective Ricci flat spherically symmetric Finsler metrics

2018 ◽  
Vol 29 (11) ◽  
pp. 1850078 ◽  
Author(s):  
Hongmei Zhu ◽  
Haixia Zhang
Keyword(s):  
Ricci Curvature ◽  
Finsler Geometry ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Spherically Symmetric ◽  
Projective Invariant ◽  
Ricci Flat ◽  
Douglas Metric

In Finsler geometry, the projective Ricci curvature is an important projective invariant. In this paper, we characterize projective Ricci flat spherically symmetric Finsler metrics. Under a certain condition, we prove that a projective Ricci flat spherically symmetric Finsler metric must be a Douglas metric. Moreover, we construct a class of new nontrivial examples on projective Ricci flat Finsler metrics.

scholarly journals Fiberwise convexity of Hill’s lunar problem

2017 ◽  
Vol 09 (04) ◽  
pp. 571-630 ◽  
Author(s):  
Junyoung Lee
Keyword(s):  
Energy Level ◽  
Contact Structure ◽  
Finsler Geometry ◽  
Critical Energy ◽  
Critical Value ◽  
Finsler Metrics ◽  
Tight Contact ◽  
Systolic Inequality ◽  
Geodesic Problem ◽  
Hill's Lunar Problem

In this paper, we prove the fiberwise convexity of the regularized Hill’s lunar problem below the critical energy level. This allows us to see Hill’s lunar problem of any energy level below the critical value as the Legendre transformation of a geodesic problem on [Formula: see text] with a family of Finsler metrics. Therefore the compactified energy hypersurfaces below the critical energy level have the unique tight contact structure on [Formula: see text]. Also one can apply the systolic inequality of Finsler geometry to the regularized Hill’s lunar problem.

scholarly journals A NEW QUANTITY IN RIEMANN-FINSLER GEOMETRY

2012 ◽  
Vol 54 (3) ◽  
pp. 637-645 ◽  
Author(s):  
XIAOHUAN MO ◽  
ZHONGMIN SHEN ◽  
HUAIFU LIU
Keyword(s):  
Scalar Curvature ◽  
Simple Proof ◽  
Finsler Geometry ◽  
Finsler Manifold ◽  
Flag Curvature ◽  
Finsler Metric ◽  
Finsler Metrics ◽  
Riemannian Curvature

AbstractIn this note, we study a new Finslerian quantity Ĉ defined by the Riemannian curvature. We prove that the new Finslerian quantity is a non-Riemannian quantity for a Finsler manifold with dimension n = 3. Then we study Finsler metrics of scalar curvature. We find that the Ĉ-curvature is closely related to the flag curvature and the H-curvature. We show that Ĉ-curvature gives, a measure of the failure of a Finsler metric to be of weakly isotropic flag curvature. We also give a simple proof of the Najafi-Shen-Tayebi' theorem.

On general (α,β)-metrics of Landsberg type

2016 ◽  
Vol 13 (06) ◽  
pp. 1650085 ◽  
Author(s):  
M. Zohrehvand ◽  
H. Maleki
Keyword(s):  
General Formula ◽  
Open Problem ◽  
Finsler Geometry ◽  
Riemannian Metric ◽  
Finsler Metrics

In this paper, we study a class of Finsler metrics, which are defined by a Riemannian metric [Formula: see text] and a one-form [Formula: see text]. They are called general [Formula: see text]-metrics. We have proven that, every Landsberg general [Formula: see text]-metric is a Berwald metric, under a certain condition. This shows that the hunting for an unicorn, one of the longest standing open problem in Finsler geometry, cannot be successful in the class of general [Formula: see text]-metrics.

On a class of projective Ricci flat Finsler metrics

2017 ◽  
Vol 90 (1-2) ◽  
pp. 169-180 ◽  
Author(s):  
Xinyue Cheng ◽  
Yuling Shen ◽  
Xiaoyu Ma
Keyword(s):  
Finsler Metrics ◽  
Ricci Flat

On Some Non-Riemannian Quantities in Finsler Geometry

2013 ◽  
Vol 56 (1) ◽  
pp. 184-193 ◽  
Author(s):  
Zhongmin Shen
Keyword(s):  
Finsler Geometry ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Geometric Properties

AbstractIn this paper we study several non-Riemannian quantities in Finsler geometry. These non- Riemannian quantities play an important role in understanding the geometric properties of Finsler metrics. In particular, we study a new non-Riemannian quantity defined by the S-curvature. We show some relationships among the flag curvature, the S-curvature, and the new non-Riemannian quantity.

scholarly journals On a projectively invariant pseudo-distance in Finsler geometry

2015 ◽  
Vol 12 (04) ◽  
pp. 1550043 ◽  
Author(s):  
Behroz Bidabad ◽  
Maryam Sepasi
Keyword(s):  
Nonlinear Analysis ◽  
Ricci Tensor ◽  
Finsler Geometry ◽  
Finsler Metrics ◽  
Analysis Method ◽  
Covariant Derivatives

Here, a nonlinear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci tensor and its covariant derivatives.

scholarly journals A class of Randers metrics of scalar flag curvature

2020 ◽  
Vol 31 (13) ◽  
pp. 2050114
Author(s):  
Xinyue Cheng ◽  
Li Yin ◽  
Tingting Li
Keyword(s):  
Necessary Conditions ◽  
Finsler Geometry ◽  
Classification Problem ◽  
Flag Curvature ◽  
Finsler Metrics ◽  
Randers Metrics

One of the most important problems in Finsler geometry is to classify Finsler metrics of scalar flag curvature. In this paper, we study the classification problem of Randers metrics of scalar flag curvature. Under the condition that [Formula: see text] is a Killing 1-form, we obtain some important necessary conditions for Randers metrics to be of scalar flag curvature.

scholarly journals On the ℒ-duality of a Finsler space with exponential metric αeβ/α

2018 ◽  
Vol 10 (1) ◽  
pp. 167-177
Author(s):  
Ramdayal Singh Kushwaha ◽  
Gauree Shanker
Keyword(s):  
Finsler Space ◽  
Finsler Geometry ◽  
Riemannian Metric ◽  
Finsler Metrics ◽  
Exponential Metric

Abstract The (α, β)-metrics are the most studied Finsler metrics in Finsler geometry with Randers, Kropina and Matsumoto metrics being the most explored metrics in modern Finsler geometry. The ℒ-dual of Randers, Kropina and Matsumoto space have been introduced in [3, 4, 5], also in recent the ℒ-dual of a Finsler space with special (α, β)-metric and generalized Matsumoto spaces have been introduced in [16, 17]. In this paper, we find the ℒ-dual of a Finsler space with an exponential metric αeβ/α, where α is Riemannian metric and β is a non-zero one form.

A class of Ricci-flat Finsler metrics

2018 ◽  
Vol 121 (1) ◽  
pp. 73-83
Author(s):  
Semail Ülgen ◽  
Esra S. Sevim
Keyword(s):  
Finsler Metrics ◽  
Ricci Flat
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