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