Abstract
LetF n be a Finsler space with metric functionF(x, y). M. Matsumoto [6] has defined a modified Finsler spaceF *n whose metric functionF *(x, y) is given byF *2 = = F2 + (Xi(x)yi)2, whereX i are the components of a covariant vector which is a function of coordintae only. Since a concurrent vector is a function of coordinate only, Matsumoto and Eguchi [9] have studied various properties of the modified Finsler spaceF *n under the assumption thatX i are the components of a concurrent vector field inF n. In this paper we shall introduce the concept of semi-parallel vector field inF n and study the properties of modified Finsler spaceF *n .
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Adati, On subprojective spaces, I,Tôhoku Math. J. 2 (1951), 159–173.MR 14—86
G. M. Fulton, Parallel vector fields.Proc. Amer. Math. Soc. 16 (1965), 136–137.MR 30 # 2435
M. Hashiguchi, Semi symmetric connections and spaces of negative constant curvature,Science Reports of Kagoshima Univ. 15 (1966), 7–11.MR 35 # 4851
H. Izumi, OnP *-Finsler spaces, I,Memo. Defence Academy,16 (1976), 133–138.
M. Matsumoto, The theory of Finsler connections,Publ. of the study group of geometry,5, College of Liberal Arts and Science, Okayama Univ. (1970).MR 42 # 2409
M. Matsumoto, On some transformation of locally Minkowskian spaces,Tensor, N. S. 22 (1971), 103–111.MR 43 # 2651
M. Matsumoto, On Finsler spaces with curvature tensors of some special forms,Tensor, N. S. 22 (1971), 201–204.MR 45 # 1096
M. Matsumoto, Onh-isotropic andC h-recurrent Finsler spaces,J. Math. Kyoto Univ. 11 (1971), 1–9.MR 42 # 6769
M. Matsumoto andK. Eguchi, Finsler space admitting a concurrent vector field,Tensor, N. S. 28 (1974), 239–249.MR 50 # 14557
M. Matsumoto andH. Shimada, On Finsler spaces with the curvature tensorsP hijk andS hijk satisfying special conditions,Reports on Math. Physics 12 (1977), 77–82.MR 57 # 4036
S. Numata, On the torsion tensorsR hjk andP hjk of Finsler spaces with the metricds = (gij(dx)dxidxj)1/2 + bi(x)dxi,Tensor, N. S. 32 (1978), 27–31.MR 57 # 53029
B. N. Prasad, Finsler spaces with the torsion tensorP ijk of a special form,Indian J. Pure Appl. Math. 11 (12) (1980), 1572–1579.
B. N. Prasad andB. Singh, On concircular vector fields in Finsler space,J. Math. Phys. Sci. 14 (1980). (Under publication)
H. Rund,The differential geometry of Finsler spaces, Springer, Berlin, 1959.MR 21 # 4462
S. Tachibana, On Finsler spaces which admit a concurrent vector field,Tensor, N. S. 1 (1950), 1–5.MR 12—749
K. Yano, Sur le parallelisme et la concourance dans l'espaces de Riemann,Proc. Imp. Acad. Tokyo 19 (1943), 149–197.MR 7—264
K. Yano, On the torse forming directions in Riemannian spaces,Proc. Imp. Acad. Tokyo 20 (1944), 340–345.MR 7—331
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Singh, U.P., Prasad, B.N. Modification of a Finsler space by a normalized semi-parallel vector field. Period Math Hung 14, 31–41 (1983). https://doi.org/10.1007/BF02023579
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02023579