• 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.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.1-16
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• 2018

In this paper, we give characteristic differential equations of a kind of projective vector fields on Finsler manifolds. Using these equations, we prove the vanishing theorem of projective vector fields on any compact Finsler manifold with the negative mean Ricci curvature, which is defined in [10]. This result involves the vanishing theorem of Killing vector fields in the Riemannian case and the work of [1, 14].

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.421-437
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• 2019

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.137-145
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• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.879-897
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• 2024

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning (𝛼, 𝛽)-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this research paper, we have conducted an investigation into the generalized square metric denoted as $F(x,y)=\frac{[{\alpha}(x,y)+{\beta}(x,y)]^{n+1}}{[{\alpha}(x,y)]^n}$, focusing specifically on its application to the Finslerian hypersurface. Furthermore, the classification and existence of first, second, and third kind of hyperplanes of the Finsler manifold has been established.

• East Asian mathematical journal
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• v.11 no.2
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• pp.315-319
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.49-55
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• 2012

In this paper, we prove that a complex Finsler manifold is a complex locally Minkowski space if and only if it is a strictly K$\ddot{a}$hler-Berwald manifold with zero holomorphic sectional curvature.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1335-1349
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• 2020

In this paper, we give an equivalent characterization for general (α, β)-metrics with reversible geodesics when the dimension of the manifold is greater than 2.

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

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.593-607
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• 2021

The aim of the present paper is to establish an intrinsic generalization of Cartan connection in Finsler geometry. This connection is called the vertical recurrent Finsler connection. An intrinsic proof of the existence and uniqueness theorem for such connection is investigated. Moreover, it is shown that for such connection, the associated semi-spray coincides with the canonical spray and the associated nonlinear connection coincides with the Barthel connection. Explicit intrinsic expression relating this connection and Cartan connection is deduced. We also investigate some applications concerning the fundamental geometric objects associated with this connection. Finally, three important results concerning the curvature tensors associated to a special vertical recurrent Finsler connection are studied.