ON FINSLER SPACES WITH A KROPINA METRIC AND SPECIAL FORMS OF IMPORTANT TENSORS
Keywords:
Abstract
In this paper we have discuss the Finsler spaces (Mn;L) and
(Mn; L), here L(x; y) is obtained from L(x; y) by L(x; y) =
L2(x; y)
(x; y)
,
where (x; y) = bi(x)dxi is a dierential one-form given on Mn.
The purpose of the present paper is to write the various tensors of
L(x; y) in terms of the tensors of L(x; y). Further, we have discuss
beauty of various curvature torsion tensors of L(x; y) when L(x; y) is
Riemannian i.e. L(x:y) is in terms of well known Kropina metric.
Mathematics subject Classication: 53B40, 53C60.
Keywords: Kropina metric, Cartan connection,C-reducibility and
curvature tensor.
References
P.N.Pandey and M.K.Gupta: Finsler Space subjected to a Kropina
change with an h-vector, arXiv:1404.6324vl[math.DG](2014).
M.K.Gupta and P.N.Pandey:Hypersurfaces of conformally
and h-conformally related Finsler spaces, Acta Math. Hungar,
(3)(2009); 257 264:
M.K.Gupta and P.N.Pandey: On hypersurface of a Finsler space
with a special metric, Acta Math. Hungar, 120(1 2)(2008); 165 177:
P. L. Antonelli, R. S. Ingarden and M. Matsumoto: The theory
of Sprays and Finsler spaces with applications in Physics and Biology,
Kluwer Acad. Publishers, Dordrecht / Boston / London,1993.
B.N. Prasad :On the torsion tensors Rhjk and Phjk of Finsler spaces
with a metric ds = (gij(dx) dxi dxj)1/2 + bi(x, y) dxi, Indian J. pure
appl. Math. 21 1(1990); 27 39:
M.Matsumoto: Foundation of Finsler geometry and special Finsler
spaces, Kaisesiha Press, Saikawa, Otsu,Japan,1986:
C. Shibata: On invariant tensors of changes of Finsler metric, J.
Math. Kyoto Univ. 24 1(1984); 163 188:
H. Izumi: Conformal transformations of Finsler spaces II. An h-
conformally
at Finsler space, Tensor N.S. 34 (1980), 337-359.
C. Shibata: On Finsler spaces with Kropina metric, Rep. Math. Phys.
(1978), 117-128.
M.Matsumoto: On Finsler spaces with Rander's metric and special
forms of important tensors, J.Math.Kyoto Univ.14 3(1974)477 498:
Matsumoto,M: On C-Reducible Finsler Spaces. Tensor,
N.S.24(1972); 29 37.
Kawaguchi,H: On Finsler spaces with the vanishing second curvature
tensor. Tensor, N.S. 26(1972); 250 254
M. Matsumoto: On Finsler Spaces with curvature tensor of some
special forms. Tensor, N.S. 22(1971); 201 204.
M. Matsumoto: The theory of Finsler connections. Publ. Study Group
Geometry 5(1970); 214 pp. Department of Math, College of Liberal Arts
and Sciences, Okayama University.
Ingarden,R.S.: On the geometrically absolute representation in the
electron microscope. Trav.Soc.Sci.Lett.Wroclaw,B 45(1957); 60pp:
Decike,A.: Uber die Finsler-Ramue mit Ai = 0:, Arch.Math.
(1953); 45 51:
Downloads
Published
Issue
Section
License
Copyright Notice
Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication.
Copyrights for articles published in World Scholars journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
