Open Access Subscription Access
Open Access Subscription Access
Four-Dimensional Conformally Flat Berwald and Landsberg Spaces
The problem of conformal transformation and conformal flatness of Finsler spaces has been studied in , , , , . Recently, Prasad et. al  have studied three dimensional conformally flat Landsberg and Berwald spaces and have obtained some important results. The purpose of the present paper is to extend the idea of conformal change to four dimensional Finsler spaces and find the suitable conditions under which a four dimensional conformally at Landsberg space becomes a Berwald space.
Miron Frame, Conformal Transformation, Conformally Flat Spaces, Berwald Spaces, Landsberg Spaces.
- S. Akbulut and M. Kalafat, A class of locally conformally at 4-manifolds, New York J. Math. 18 (2012), 733-763.
- P. L. Antonelli, Hand book of Finsler geometry, Kluwer Academic Publishers, Dordrecht, The Netherlands 2003.
- M. F. Atiyah, N. J. Hitchin and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1711), (1978), 425-461.
- Sun-Yung A. Change, Jie Qing and Paul C. Yang, Compactication of a class of conformally at 4-manifolds, Invest. Math. 142, (2000), 65-93.
- M. Gromov, H. B. Lawson and W. Thruston, Hyperbolic 4-manifolds and conformally at 3-manifolds, Publications Mathematiques del. I. H. E. S, tome 68 (1988), 27-45.
- M. Hashiguchi, On conformal transformations of Finsler metrics, J. Math. Kyoto University, 16 (1976), 85-99.
- M. Iori and R. Piergallini, 4-manifolds as covers of 4-sphere branched over nonsingular surfaces, Geom. Topol. 6 (2002), 393-401.
- M. Kalafat, Locally conformally at and self-dual structures on simple 4-manifolds, Proceedings of 19th Gokova Geo-Topo. conference, (2012), 111-122.
- M. Kapovich, Conformally at metrics on 4-manifolds, J. Dierential geometry, 66 (2004), 289-301.
- N. H. Kuiper, On conformally at spaces in large , Ann. of Math. 50(2), (1949), 916-924.
- N. H. Kuiper, On compact conformally Euclidean spaces of dimension >2, Ann. of Math. 52(2), (1950), 478-490.
- R. S. Kulkarni, Conformally at manifolds, Proc. Nat. Acad. Sci. USA 69(9), (1972), 2675-2676.
- M. Matsumoto, On C-reducible Finsler spaces, Tensor, N. S., 24 (1972), 29-37.
- M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Saikawa, Otsu, 520, Japan 1986.
- M. Matsumoto, The theory of Finsler spaces with m th-root metric II, Pub. Math. Debrecen, 49 (1996), 135-155.
- M. Matsumoto and R. Miron, On an invariant theory of Finsler spaces, Period. Math., Hunger., 8 (1977), 73-82.
- A. Moor, Uberdie Torsions-Und Krummung invarianten der dreidimensonalen Finslerschen Raume, Math Nachr., 16 (1957), 85-99.
- T. N. Pandey and D. K. Divedi, A theory of four-dimensional Finsler spaces in terms of scalars, J. Nat. Acad. Math., 11 (1997), 176-190.
- B. N. Prasad, T. N. Pandey and M. K. Singh, Three dimensional conformally at Landsberg and Berwald spaces, J. Int. Acad. Phy. Sc., 13(3), (2009), 299-309.
- B. N. Prasad and Gauree Shanker, Conformal change of four-dimensional Finsler space, Bull. Cal. Math. Soc., 102(5), (2010), 423-432.
- R. Yoshikawa and K. Okubo, Two dimensional conformally at Finsler spaces, Tensor, N. S., 60 (1998), 99-108.
Abstract Views: 3
PDF Views: 0