Curvatures on Homogeneous Generalized Matsumoto Space

Abstract

The curvature characteristics of particular classes of Finsler spaces, such as homogeneous Finsler spaces, are one of the major issues in Finsler geometry. In this paper, we have obtained the expression for S-curvature in homogeneous Finsler space with a generalized Matsumoto metric and demonstrated that the homogeneous generalized Matsumoto space with isotropic S-curvature has to vanish the S-curvature. We have also derived the expression for the mean Berwald curvature by using the formula of S-curvature.

Geometry and evolution of Hasimoto surface in Minkowski 3-space

“…In future work, we plan to investigate the harmonic evolute surfaces of the Hasimoto surface in different spaces, including Galilean and pseudo-Galilean spaces. We aim to enhance the results presented in this paper by incorporating techniques and findings from related studies [27][28][29][30][31][32][33][34][35][36][37]. Additionally, we intend to explore novel methods to discover further results and theorems concerning the singularity and symmetry properties of this topic, which will be presented in our upcoming papers.…”

On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space

“…Recently, we have obtained the formula of S-curvature for the homogeneous Finsler space with generalized Matsumoto metric [4]. For this space, we have obtained the equivalent condition under which the S-curvature has vanished.…”

“…It has notorious examples including Bogoslovsky-Kropina metrics, which represent the framework for very special relativity (VSR) and its generalization, very general relativity (VGR) [2]. The generalized Matsumoto metric ( α m+1 (α−β) m ) is studied by G. Shankar [3] and M. K. Gupta [4], etc. This metric has also numerous applications in physics such as the study of the slope of mountains [5].…”

Homology of Warped Product Semi-Invariant Submanifolds of a Sasakian Space Form with Semisymmetric Metric Connection

“…Nevertheless, multiple researchers have arrived at contrasting conclusions regarding the topological and diferentiable characteristics of submanifolds through the utilization of advanced theories such as submanifold theory and soliton theory, among others [6,12,[14][15][16][17][18]. Further inspiration for our work can be gleaned from the papers cited as references [5,9,[19][20][21][22][23][24][25][26].…”