Finslerian convolution metrics and their special classes

Document Type : Original Article

Author

Section de Mathématiques, Ecole Normale Supérieure du Burundi, Bujumbura, Burundi

Abstract

Here, it is introduced a concept of convolution metric in Finslerian Geometry. Some basic properties of the Finslerian convolution metrics are studied. Then it is characterized Finslerian convolution metrics which are of type Riemannian, Minkowskian as well as Randers. Furthermore, some examples of the Finslerian convolutions are given.

Keywords


 1. D. Bao, S.-S. Chern, and Z. Shen, An introduction to Riemann-Finsler Geometry,Springer-Verlang New York, 2000.
2. B.-Y. Chen,
Convolution of Riemannian manifolds and its applications, Bull. Austral.Math. Soc. 66 (2002), 177-191.
3. B.-Y. Chen,
Differential Geometry of Warped Product Manifolds and Submanifolds,World Scientific Publishing, 2016.
4. W. K¨uhnel and H.-B. Rademacher,
Conformal vector fields on pseudo-Riemannian spaces, Diff. Geom. Appl. 7 (1997) 237-250.
5. G. Nibaruta, M. Karimumuryango, A. Nibirantiza and D. Ndayirukiye, Twisted products Berwald metrics of polar type, Differ. Geom.-Dyn. Syst. 22(2020), 183-193.
6. Y.-B Shen and Z. Shen,
Introduction to Modern Finsler Geometry, World Scientific Publishing, 2016.