• Journal of the Korean Mathematical Society
• /
• v.38 no.3
• /
• pp.503-521
• /
• 2001

A change of Finsler metric L(x,y)longrightarrowL(x,y) is called a Randers change of L, if L(x,y) = L(x,y) +$\rho$(x,y), where $\rho$(x,y) = $\rho$(sub)i(x)y(sup)i is a 1-form on a smooth manifold M(sup)n. Let us consider the special Randers change of Finsler metric LlongrightarrowL = L + $\beta$ by $\beta$. On the basis of this special Randers change, the purpose of the present paper is devoted to studying the conditions for Finsler space F(sup)n which are transformed by a special Randers change of Finsler spaces F(sup)n with ($\alpha$,$\beta$)-metrics of Douglas type to be also of Douglas type, and vice versa.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.457-464
• /
• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.337-346
• /
• 2000

The geodesic equation in a two-dimensional Finsler space is given by the differential equation of the Weierstrass form. In the present paper, we express the differential equations of geodesics in a two-dimensional Finsler space with a generalized Kropina metric.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.407-418
• /
• 2019

In this paper, we study conformal transformations between special class of Finsler metrics named C-reducible metrics. This class includes Randers metrics in the form $F={\alpha}+{\beta}$ and Kropina metric in the form $F={\frac{{\alpha}^2}{\beta}}$. We prove that every conformal transformation between locally dually flat Randers metrics must be homothetic and also every conformal transformation between locally dually flat Kropina metrics must be homothetic.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1485-1502
• /
• 2014

The explicit formula for the hyperbolic metric ${\lambda}_{{\alpha},{\beta},{\gamma}}(z){\mid}dz{\mid}$ on the thrice-punctured sphere $\mathbb{P}{\backslash}\{0,1,{\infty}\}$ with singularities of order 0 < ${\alpha}$, ${\beta}$ < 1, ${\gamma}{\leq}1$, ${\alpha}+{\beta}+{\gamma}$ > 2 at 0, 1, ${\infty}$ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$ near the origin and give more precise descriptions for the asymptotic behavior of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$.