On conformal transformation of special curvature of Kropina metrics

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Abstract
An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the special cases the conformal transformations reduced to homothetic transformations. ./files/site1/files/62/14Abstract.pdf
Keywords

1. Hashiguchi M., "On conformal transformations of Finsler metrics", J. Math. Kyoto Univ., 16 (1976) 25-50.## 2. Vincze Cs., "On the existence of C-conformal changes of Riemann–Finsler metrics", Tsukuba J. Math., 24 (2) (2000) 419-426. ## 3. Bacso S., Cheng X., "Finsler conformal transformations and the curvature invariances", , Publ. Math. Debrecen, 70/1-2, (2007) 221-231. ## 4. Xiao-ling Z., "Conformal transformation between some Finsler Einstein spaces", Journal of East China Normal Univercity (natural science) 2. ## 5. Chen G., Cheng X., Zou Y., "On conformal transformation between two (α,β)-metrics", DIfferential Geometry and its Applications, 31 (2013) 300-307. ## 6. Shen B., "S-closed conformal transformations in Finsler geometry",Differential Geometry and its Applications, 58 (2018) 254-263. ## 7. Kropina V. K., "On projective two-dimensional Finsler spaces with a special metric", Trudy Sem. Vektor. Tenzor. Anal.,11 (1961) 277-292. ##8. Akbar Zade H., "Sur less espaces de Finsler A courbures sectionnelles constants" , Acad. Roy. Belg. Bull. Cl. Sci. (5) 74 (1988) 271-322. ## 9. Najafi B., Tayebi A., " Finsler metrics of scalar Flag curvature and projective invariants", Balkan Journal of Geometry and Its Applications, Vol.15, No. 2 (2010) 82-91. ## 10. Shen Z., "On Some Non-Riemannian Quantities in Finsler Geometry", Canad. Math. Bull. 56 (2013) 184-193. ## 11. Chen G., Liu L.,"On Kropina metrics with non Riemannian curvature properties", diff geom.,43 (2015) 180-191. ##