homogeneous finsler space
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Author(s):  
Sarita Rani ◽  
Gauree Shanker

The study of curvature properties of homogeneous Finsler spaces with $(\alpha, \beta)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on a homogeneous Finsler space with Randers changed square metric has been proved. Further, an explicit formula for $S$-curvature of Randers changed square metric has been established. Finally, using the formula of $S$-curvature, the mean Berwald curvature of afore said $(\alpha, \beta)$-metric has been calculated. 


2020 ◽  
Vol 20 (3) ◽  
pp. 391-400
Author(s):  
Gauree Shanker ◽  
Kirandeep Kaur

AbstractWe prove the existence of an invariant vector field on a homogeneous Finsler space with exponential metric, and we derive an explicit formula for the S-curvature of a homogeneous Finsler space with exponential metric. Using this formula, we obtain a formula for the mean Berwald curvature of such a homogeneous Finsler space.


2020 ◽  
Vol 17 (02) ◽  
pp. 2050019
Author(s):  
Gauree Shanker ◽  
Sarita Rani

The study of curvature properties of homogeneous Finsler spaces with [Formula: see text]-metrics is one of the central problems in Riemann–Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for [Formula: see text]-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of [Formula: see text]-curvature, the mean Berwald curvature of aforesaid [Formula: see text]-metric is calculated.


2017 ◽  
Vol 13 (02) ◽  
pp. 47-53
Author(s):  
Chandru K. ◽  
Narasimhamurthy S.K.

2014 ◽  
Vol 57 (2) ◽  
pp. 457-464 ◽  
Author(s):  
MING XU ◽  
SHAOQIANG DENG

AbstractIn this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature. In the special case that the homogeneous Finsler space is a Randers space, we give an explicit formula which coincides with the previous formula obtained by the second author using other methods.


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