Finslerian metrics locally conformally R-Einstein

Document Type : Original Article

Authors

1 Filiere de Mathematiques et informatique, Ecole Normale Sup´erieure de Natitingou, Benin

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

3 Institut de Mathématiques et de Sciences Physiques, Centre d'Excellence, Porto-Novo, Bénin

Abstract

Let R be the hh-curvature associated with the Chern connection or the Cartan connection. Adopting the pulled-back tangent bundle approach to the Finslerian Geometry, an intrinsic characterization of R-Einstein metrics is given. Finslerian metrics which are locally conformally R-Einstein are classified

Keywords


 1. P. L. Antonelli, R. S. Ingarden and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Academic Publishers, Dordrecht, 1993.
2. D. Bao, S.-S. Chern, and Z. Shen,
An introduction to Riemann-Finsler Geometry, Springer-Verlang New York, (2000), 1-192.
3. D. Bao and C. Robles,
Ricci and Flag Curvatures in Finsler Geometry, MSRI Publications, 50 (2004).
4. A. L. Besse,
Einstein Manifolds, Springer-Verlag Berlin Heidelberg, (1987), 1-528.
5. H. W. Brinkmann,
Riemann spaces conformal to Einstein spaces, Proc. Nat. Acad. Sci.USA, 9 (1923), 172-174.
6. C. N. Kozameh, E. T. Newman and K. P. Tod,
Conformal Einstein Spaces, Gen. Rel.and Grav., 17 (1985), 343-344.
7. M. Listing,
Conformal Einstein Spaces in N-dimensions, Ann. Glob. Anal. Geom.,20(2001), 183-197.
8. F. Massamba and J. S. Mbatakou,
Induced and intrinsic Hashiguchi connections on Finsler submanifolds, Balkan J. Geom. Appl., 22(2) (2017), 50-62.
9. J.-S. Mbatakou,
Intrinsic proofs of the existence of generalized Finsler connections, Int.Electron. J. Geom., 8, 1 (2015), 1-13.
10. G. Nibaruta, S. Degla and L. Todjihounde,
Prescribed Ricci tensor in Finslerian conformal class, Balkan J. Geom. Appl., 23, 2 (2018), 41-55.
11. G. Nibaruta, S. Degla and L. Todjihounde,
Finslerian Ricci Deformation and Conformal Metrics, J. Appl. Math. Phys., 6 (2018), 1522-1536.
12. W. K¨uhnel and H.-B. Rademacher,
Conformally Einstein product spaces, E-print 2016,1-35.
13. Y.-B. Shen and Z. Shen,
Introduction to Modern Finsler Geometry, Higher Education Press Limited Company and World Scientific Publishing Co. Pte. Ltd. (2016), 1-58.
14. P. Szekeres,
Spaces Conformal to a Class of Spaces in General Gelativity, Proc. Roy. Soc. London, Ser. A., 274 (1963), 206-212.