scholarly journals RETRACTED: Sasaki–Randers metric in Finsler geometry

2012 ◽  
Vol 387 (2) ◽  
pp. 1137-1145 ◽  
Author(s):  
E. Peyghan ◽  
A. Tayebi
Keyword(s):  
Finsler Geometry ◽  
Randers Metric

ON COMPLEX RANDERS METRICS

2010 ◽  
Vol 21 (08) ◽  
pp. 971-986 ◽  
Author(s):  
BIN CHEN ◽  
YIBING SHEN
Keyword(s):  
Finsler Geometry ◽  
Randers Metric ◽  
Holomorphic Curvature ◽  
Randers Metrics

A characteristic for a complex Randers metric to be a complex Berwald metric is obtained. The formula of the holomorphic curvature for complex Randers metrics is given. It is shown that a complex Berwald Randers metric with isotropic holomorphic curvature must be either usually Kählerian or locally Minkowskian. The Deicke and Brickell theorems in complex Finsler geometry are also proved.

SOME RESULTS ON THE NON-RIEMANNIAN QUANTITY H OF A FINSLER METRIC

2011 ◽  
Vol 22 (07) ◽  
pp. 925-936 ◽  
Author(s):  
QIAOLING XIA
Keyword(s):  
Finsler Geometry ◽  
Finsler Manifold ◽  
Finsler Metric ◽  
Randers Metric ◽  
Rigidity Theorems

In this paper, we study the non-Riemannian quantity H in Finsler geometry. We obtain some rigidity theorems of a compact Finsler manifold under some conditions related to H. We also prove that the S-curvature for a Randers metric is almost isotropic if and only if H almost vanishes. In particular, S-curvature is isotropic if and only if H = 0.

scholarly journals Weighted projective Ricci curvature in Finsler geometry

2021 ◽  
Vol 71 (1) ◽  
pp. 183-198
Author(s):  
Tayebeh Tabatabaeifar ◽  
Behzad Najafi ◽  
Akbar Tayebi
Keyword(s):  
Ricci Curvature ◽  
Finsler Geometry ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Randers Metric ◽  
Ricci Flat ◽  
Projectively Flat ◽  
Flat Metric ◽  
Necessary And Sufficient ◽  
Randers Metrics

Abstract In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted projective Ricci flat curvature. Finally, we show that every projectively flat metric with isotropic weighted projective Ricci and isotropic S-curvature is a Kropina metric or Randers metric.

Cheng–Shen conjecture in Finsler geometry

2020 ◽  
Vol 31 (04) ◽  
pp. 2050030
Author(s):  
M. Atashafrouz ◽  
B. Najafi
Keyword(s):  
Lie Groups ◽  
Finsler Geometry ◽  
Three Dimensional ◽  
Closed Manifold ◽  
Classification Theorem ◽  
Randers Metric ◽  
Counter Example ◽  
Randers Metrics

The well-known Cheng–Shen conjecture says that every [Formula: see text]-quadratic Randers metric on a closed manifold is a Berwald metric. The class of [Formula: see text]-quadratic Randers metrics contains the class of generalized Douglas–Weyl Randers metrics. In this paper, we give a classification of left-invariant Randers metrics of generalized Douglas–Weyl type on three-dimensional Lie groups. Based on our classification theorem, we find a counter-example for the Cheng–Shen conjecture.

On generalized Einstein Randers metrics

2015 ◽  
Vol 12 (10) ◽  
pp. 1550105 ◽  
Author(s):  
Akbar Tayebi ◽  
Ali Nankali
Keyword(s):  
Finsler Geometry ◽  
Riemannian Metric ◽  
Einstein Metric ◽  
Randers Metric ◽  
Randers Metrics

In this paper, we study the Ricci directional curvature defined by H. Akbar-Zadeh in Finsler geometry and obtain the formula of Ricci directional curvature for Randers metrics. Let F = α + β be a Randers metric on a manifold M, where [Formula: see text] is a Riemannian metric and β = biyi is a closed 1-form on M. We prove that F is a generalized Einstein metric if and only if it is a Berwald metric.

NEW CANDIDATES FOR A HERMITIAN APPROACH OF GRAVITY

2013 ◽  
Vol 10 (09) ◽  
pp. 1350041 ◽  
Author(s):  
NICOLETA ALDEA ◽  
GHEORGHE MUNTEANU
Keyword(s):  
Field Theory ◽  
Finsler Geometry ◽  
Finsler Metrics ◽  
Quantum Field ◽  
Schwarzschild Metric ◽  
Curved Space ◽  
Gravitational Fields ◽  
Randers Metric ◽  
Klein Gordon ◽  
Complex Finsler Metrics

In this paper, some possible candidates for the study of gravity are proposed in terms of complex Finsler geometry. These mainly concern the complex Hermitian versions of weakly gravitational metric and Schwarzschild metric. For the weakly gravitational fields, we state few interesting geometrical and physical aspects such as the conditions under which a complex Finsler metrics are projectively related to the weakly gravitational metric. In the Kähler case, the geodesic curves of the weakly gravitational metric are obtained. Some applications concerning the deformations of the weakly gravitational Hermitian metric to a complex Randers metric are described. Another candidate for gravity is given by so-called Hermitian Schwarzschild metric for which some geodesic curves are highlighted. The last part of the paper is devoted to a generalization of the complex Klein–Gordon equations, in terms of Quantum field theory on a curved space.

scholarly journals Finsler geometry modeling of complex fluids: reduction in viscous resistance

2021 ◽  
Vol 1730 (1) ◽  
pp. 012036
Author(s):  
Masahiko Okumura ◽  
Ippei Homma ◽  
Shuta Noro ◽  
Hiroshi Koibuchi
Keyword(s):  
Complex Fluids ◽  
Finsler Geometry ◽  
Viscous Resistance ◽  
Geometry Modeling

scholarly journals Finsler geometry modeling for anisotropic diffusion in Turing patterns

2021 ◽  
Vol 1730 (1) ◽  
pp. 012035
Author(s):  
Hiroshi Koibuchi ◽  
Masahiko Okumura ◽  
Shuta Noro
Keyword(s):  
Anisotropic Diffusion ◽  
Finsler Geometry ◽  
Turing Patterns ◽  
Geometry Modeling

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

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