PROJECTIVE CHANGE BETWEEN RANDERS METRIC AND EXPONENTIAL (A, B)-METRIC

Ganga Prasad Yadav, Paras Nath Pandey

DOI Number
https://doi.org/10.22190/FUMI1803389Y
First page
389
Last page
399

Abstract


In this paper, we find the conditions to characterize projective change between two  (A, B)-metrics, such as exponential (A, B)-metric,  and Randers metric L=A+B on a manifold with dim n > 2, where A and A are two Riemannian metrics, B and B are two non-zero 1-forms. Further, we discussed the special curvature properties of two classes of (A, B)-metrics.

 


Keywords

Finsler space, (A, B)-metric, projective change, Randers metric, Berwlad, Riemannian metric.

Keywords


Finsler space, (A, B )-metric, Projective change, Randers metric, Berwlad, Riemannian metric.

Full Text:

PDF

References


A. Rapscak: Uber die bahntreuen abbildungen metrisher. Publ. Math. Debrecen

(1961), 285{290.

H. S. Park and Y. Lee: Projective change between a Finsler space with (; ){

metric and the associated Riemannian metric. Canad. J. Math. 60 (2008), 443{

H. S. Park and I. Y. Lee: On projectively

at Finsler spaces with (; ){metric.

Commun. Korean Math. Soc. 14(2) (1999), 373{383.

H. S. Park and Il-Yong Lee: The Randers changes of Finsler spaces with

(; ){metrics of Douglas type. J. Korean math. Soc. 38(3) (2001), 503{521.

H. Rund: The Dierential Geometry of Finsler Spaces. Springer-Verlag, Berlin,

Projective Change between Randers Metric and Exponential (; )-metric 11

M. Matsumoto: Projective

at Finsler spaces with (; ){metric. Rep. on Math.

Phys. 30 (1991), 15{20.

M. Hashiguchi and Y. Ichijyo: On some special (; )-metrics. Rep. Fac. Sci.

Kagoshima Univ. 8 (1975), 39{46.

M. Matsumoto and X. Wei: Projective change of Finsler spaces of constant

curvature. Publ. Math. Debrecen 44 (1994), 175{181.

M. Matsumoto: Foundation of Finsler Geometry and Special Finsler Spaces.

Kaiseisha Press, Otsu, Saikawa, 1986.

M. Hashiguchi and Y. Ichijiyo: Randers spaces with rectilinear geodesics. Rep.

Fac. Sci. Kagasima Univ. 13 (1980), 33{40.

Ningwei Cui and Yi{Bing Shen: Projective change between two classes of

(; ){metrics. Di. Geom. and its Applications 27 (2009), 566{573.

N. Cui: On the S{curvature of some (; ){metrics. Acta Math. Sci. 26A(7)

(2006), 1047{1056.

P. L. Antonelli, R. S. Ingarden and M. Matsumoto: The Theory of Sprays

and Finsler Spaces with Application in Physics and Biology. Kluwer Academic

Publishers, London, 1985.

S. Bacso and M. Matsumoto: Projective change between Finsler spaces with

(; ){metric. Tensor N. S. 55 (1994), 252{257.

S. Bacso, X. Cheng and Z. Shen: Curvature properties of (; ){metric. (2006).

Z. Shen and G. C. Yildirim: On a class of projectively

at matrics with constant

ag curvature. Canadian Journal of Mathematics 60(2) (2008), 443{456.

Z. Shen: On Landsberg (; ){metrics. (2006).




DOI: https://doi.org/10.22190/FUMI1803389Y

Refbacks





© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)