• 대한수학회보
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• 제56권2호
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• pp.407-418
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• 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.

• 대한수학회논문집
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• 제12권4호
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• pp.975-984
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• 1997

In the Finsler space with an $(\alpha, \beta)$-metric, we can consider the difference tensors of the Finsler connection. The properties of the conformal transformation of these difference tensors are investigated in the present paper. Some conformal invariant tensors are formed in the Finsler space with an $(\alpha, \beta)$-metric related with the difference tensors.

• 대한수학회보
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• 제55권4호
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• 한국수학사학회지
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• 제14권1호
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• pp.109-114
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• 2001

Using Fermi coordinate and Jacobi operator on Kahler manifold, we characterize partially conformal geodesic transformation in Kahler geometry.

• 대한수학회논문집
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• 제12권2호
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• pp.347-354
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• 1997

The conharmonic transforamtion is a conformal transformation which satisfies a specified differential equation. Such a transformation was defined by Y. Ishi and we generalize his results. In particular, we obtain a necessary and sufficient condition for the invariance of critical Riemannian metrics under the conharmonic transformation.

• 한국지리정보학회지
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• 제7권3호
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• pp.48-56
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• 2004

본 연구에서는 실시간 측지계 변환 기법을 사용하는 지리정보시스템에 사용될 고속 변환 모델 개발을 수행하였다. 한 측지계에 준거하여 구축된 지리정보데이터를 다른 측지계에 준거하여 표시하는 경우 원 구축데이터의 좌표를 변환시키지 않고, 화면 표시나 출력 직전에 변환하여 표시하는 방법이 사용된다. 본 연구에서는 이러한 실시간 측지계 변환 작업의 속도를 향상시키고 높은 변환 정확도를 유지하기 위한 방법으로, 지역 분할 변환 매개변수 계산에 의한 2차원 동각상사변환 모델의 적용 방안을 검토하였다. 연구 결과 일정한 범위 안에서는 비교적 많은 계산 시간을 필요로 하는 3차원 측지계 변환과 2차원 등각상사변환이 거의 동일한 변환 정확도를 나타내었으며, 영역분할에 의한 2차원 상사 변환 모델을 적용할 경우 높은 정확도를 유지하고 향상된 변환 속도를 나타내는 실시간 측지계 변환이 가능하다는 결과를 얻게 되었다.

• 대한수학회논문집
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• 제38권3호
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• pp.865-880
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• 2023

The main intention of the current paper is to characterize certain properties of *-conformal Ricci solitons on non-coKähler (𝜅, 𝜇)-almost coKähler manifolds. At first, we find that there does not exist *-conformal Ricci soliton if the potential vector field is the Reeb vector field θ. We also prove that the non-coKähler (𝜅, 𝜇)-almost coKähler manifolds admit *-conformal Ricci solitons if the potential vector field is the infinitesimal contact transformation. It is also studied that there does not exist *-conformal gradient Ricci solitons on the said manifolds. An example has been constructed to verify the obtained results.

• 한국수학사학회지
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• 제16권3호
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• pp.109-114
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• 2003

In this paper, we deal with partially conformal geodesic transformations in Kahler geometry by using Fermi coordinates when tile submanifold is a geodesic sphere. We derive the necessary and sufficient condition for tile existence of such transformation in terms of the Jacobi operator and its derivative.

• 대한수학회보
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• 제59권1호
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• pp.101-110
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• 2022

In this article, the notion of *-conformal Ricci soliton is defined as a self similar solution of the *-conformal Ricci flow. A Sasakian 3-metric satisfying the *-conformal Ricci soliton is completely classified under certain conditions on the soliton vector field. We establish a relation with Fano manifolds and proves a homothety between the Sasakian 3-metric and the Berger Sphere. Also, the potential vector field V is a harmonic infinitesimal automorphism of the contact metric structure.

• 대한수학회논문집
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• 제13권4호
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• pp.817-823
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• 1998

In the present paper, we study conformal and projective Killing vector fields and infinitesimal Q-transformations on a quaternionic Kahlerian manifold, and prove that an infinitesimal conformal or projective automorphism in a compact quaternionic Kahlerian manifold is necessarily infinitesimal automorphism.