• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.415-421
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• 1996

In this paper, we shall find the conditions that the Finsler space with a special $(\alpha,\beta)$-metric be a Riemannian space and a Berwald space.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.369-379
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• 2017

In this paper, we shall study the existence and distribution of conjugate points in Finsler geometry from the viewpoint of the oscillation and Morse index theory.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.217-224
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• 1999

In this paper the properties of the Finsler metrics compatible with an f-structure are investigated.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.339-348
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• 2000

We introduce the notion of the Finsler metrics compat-ible with a special Riemannian structure f of type (1,1) satisfying f6+f2=0 and investigate the properties of Finsler space with them.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1359-1370
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• 2022

In this paper, we study the Finsler warped product metric which is dually flat or projectively flat. The local structures of these metrics are completely determined. Some examples are presented.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.82-91
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• 2023

In this paper, we study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact Finsler manifolds with zero boundary condition, and estimate the lower bound of the first eigenvalues for (p, q)-Laplace operators on Finsler manifolds.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.237-247
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• 2007

In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which has the horizontal torsion in a special form. With this connection, we define a holomorphic sectional curvature. Then we show that this holomorphic sectional curvature of an almost complex submanifold is not greater than that of the ambient manifold. This fact, in turn, implies that a Rizza manifold is hyperbolic if its holomorphic sectional curvature is bounded above by -1.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2119-2139
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• 2017

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.303-315
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• 2001

In this paper, we investigate the topology of complex Finsler manifolds. For a complex Finsler manifold (M, F), we introduce a certain condition on the Finsler metric F on M. This is a generalization of Kahler condition for the Hermitian metric. Under this condition, we can produce a Kahler metric on M. This enables us to use the usual techniques in the Kahler and Riemannian geometry. We show that if the holomorphic sectional curvature of $ M is\geqC^2>0\; for\; some\; c>o,\; then\; diam(M)\leq\frac{\pi}{c}$ and hence M is compact. This is a generalization of the Bonnet\`s theorem in the Riemannian geometry.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.177-183
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• 2006

The purpose of this paper is to introduce an L-metrical non-linear connection $N_j^{*i}$ and investigate a conformal change in the Finsler space with $({\alpha},\;{\beta})-metric$. The (v)h-torsion and (v)hvtorsion in the Finsler space with L-metrical connection $F{\Gamma}^*$ are obtained. The conformal invariant connection and conformal invariant curvature are found in the above Finsler space.