• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.183-200
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• 2012

In the present paper, we consider the condition that is a geodesic equation on a Finsler space with an (${\alpha},\;{\beta}$)-metric. Next we find the conditions that are equations of geodesic on the Finsler space with an approximate infinite series (${\alpha},\;{\beta}$)-metric.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.649-658
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• 2001

We shall find the condition for a Finsler space with a special ($\alpha$.$\beta$)-metric L($\alpha$.$\beta$) satisfying L$^2$ =2$\alpha$$\beta$ to be a Douglas space. The special Randers change of the above Finsler metric by $\beta$ is also studied.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.353-362
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• 2019

In this paper, we study general (${\alpha}$, ${\beta}$) Finsler metrics and prove that every general (${\alpha}$, ${\beta}$)-metric is semi C-reducible but not C2-like. As a consequence of this result we prove that every general (${\alpha}$, ${\beta}$)-metric satisfying the Ricci flow equation is Einstein.

• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.603-613
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• 2023

In this paper, the concept of geodesic centered tractography is explored for diffusion tensor imaging (DTI). In DTI, where geodesics has been tracked and the inverse of the fourth-order diffusion tensor is inured to determine the diversity. Specifically, we investigated geodesic tractography technique for High Angular Resolution Diffusion Imaging (HARDI). Riemannian geometry can be extended to a direction-dependent metric using Finsler geometry. Euler Lagrange geodesic calculations have been derived by Finsler geometry, which is expressed as HARDI in sixth order tensor.

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.501-513
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• 2003

The Matsumoto metric is an ($\alpha,\;\bata$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$\mid$\beat$\mid$\;<\;$\mid$\alpha$\mid$$ by the first author. He introduced an approximate Matsumoto metric as the ($\alpha,\;\bata$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.383-391
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• 1997

The main purpose of the present paper is to derive the induced (Finsler) connections on the hypersurface from the Finsler connections of Berwald type (a Berwald h-recurrent connection and a $F\Gamma$' connection) of a Finsler space and to seek the necessary and sufficient conditions that the induced connections coincide with the intrinsic connections. And we show the quantities and relations with respect to the respective induced connections. Finally we show some examples.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.749-761
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• 2018

Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.327-340
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• 2003

We are devoted to dealing with the conformal theory of a Rizza manifold with a generalized Finsler metric $G_{ij}$ (x,y) and a new conformal invariant non-linear connection $M^{i}$ $_{j}$ (x,y) constructed from the generalized Cern's non-linear connection $N^{i}$ $_{j}$ (x,y) and almost complex structure $f^{i}$ $_{j}$ (x). First, we find a conformal invariant connection ( $M_{j}$ $^{i}$ $_{k}$ , $M^{i}$ $_{j}$ , $C_{j}$ $^{i}$ $_{k}$ ) and conformal invariant tensors. Next, the nearly Kaehlerian (G, M)-structures under conformal change in a Rizza manifold are investigate.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.699-716
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• 2009

We deal with a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric $L({\alpha},\;{\beta})$ = ${\beta}{\sum}_{k=0}^{r}(\frac{\alpha}{\beta})^k$ where ${\alpha}<{\beta}$. We introduced a Finsler space $F^n$ with an infinite series $({\alpha},{\beta})$-metric $L({\alpha},\;{\beta})=\frac{\beta^2}{\beta-\alpha}$ and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to finding the condition for a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric above to be a Douglas space.

• East Asian mathematical journal
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• v.28 no.1
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• pp.25-36
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• 2012

We introduced a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$-metric $L({\alpha},{\beta})={\beta}\sum\limits_{k=0}^r\(\frac{\alpha}{\beta}\)^k$, where ${\alpha}<{\beta}$ and investigated it with respect to Berwald space ([12]) and Douglas space ([13]). The present paper is devoted to finding the condition that is projectively at on a Finsler space $F^n$ with an approximate infinite series (${\alpha},{\beta}$)-metric above.