• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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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.

• Journal for History of Mathematics
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• v.14 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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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.

• Journal of the Korean Association of Geographic Information Studies
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• v.7 no.3
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• pp.48-56
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• 2004

This research focuses on the development of a fast datum transformation model to be used in GIS that utilizes real-time data transformation. Instance, when a GIS data constructed according to a datum is conformed to another datum, instead of transforming the axes of the original data, the data is transformed right before the results are reflected on the monitor. In this research, the prospects of calculating transformation parameters for every grid cells on the area based on two-dimensional conformal transformation model in order to decrease real-time datum transformation time while maintaining a high accuracy has been investigated. Research results showed that for a fixed area, the accuracies of the two-dimensional conformal transformation and the three-dimensional datum transformation, which requires more computing time, were almost equal and fast transformation speed, high accuracy real-time datum transformation is made feasible by implementing the grid-divided two-dimensional conformal transformation model.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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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.

• Journal for History of Mathematics
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• v.16 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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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.