On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space
Abstract
:1. Introduction
2. Preliminaries
- 0, ,
- i.e., F is positively homogeneous,
- Let be a basis of V such that Then, the Hessian matrix, , is positive definite at each point of .
3. Ricci Curvature
4. Ricci Curvature with Vanishing S-Curvature
- For the first part, let , and . Then, in view of Lemma (3), we getEquation (10) gives us , for .Since is orthonormal basis of , we obtainFor the sufficient part, letTherefore,By using the Lemma 3, is defined as
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Li, Y.; Gupta, M.K.; Sharma, S.; Chaubey, S.K. On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space. Mathematics 2023, 11, 3365. https://doi.org/10.3390/math11153365
Li Y, Gupta MK, Sharma S, Chaubey SK. On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space. Mathematics. 2023; 11(15):3365. https://doi.org/10.3390/math11153365
Chicago/Turabian StyleLi, Yanlin, Manish Kumar Gupta, Suman Sharma, and Sudhakar Kumar Chaubey. 2023. "On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space" Mathematics 11, no. 15: 3365. https://doi.org/10.3390/math11153365
APA StyleLi, Y., Gupta, M. K., Sharma, S., & Chaubey, S. K. (2023). On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space. Mathematics, 11(15), 3365. https://doi.org/10.3390/math11153365