• 대한수학회보
• /
• 제56권2호
• /
• pp.407-418
• /
• 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
• /
• 제25권2호
• /
• pp.245-249
• /
• 2010

We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.

• 대한수학회지
• /
• 제34권4호
• /
• pp.1037-1048
• /
• 1997

We show that an asymptotically Euclidean scalar-flat Kahler metric ona complex surface can be smoothly conformally compactified at the infinity point. We discuss some implication of this, characterizing such metrics on $C^2$ blown up at some points.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.857-864
• /
• 2009

The special conformally flatness is a generalization of a sub-projective space. B. Y. Chen and K. Yano ([4]) showed that every canal hypersurface of a Euclidean space is a special conformally flat space. In this paper, we study the conditions for the base space B is special conformally flat in the conharmonically flat warped product space $B^n{\times}f\;R^1$.

• 한국정밀공학회지
• /
• 제29권8호
• /
• pp.824-833
• /
• 2012

The shrinkage and the warpage of the moulded part are influenced by the design of the product and injection mould. In a flat part with a partly thick volume, the warpage of the flat part is created from the difference of the shrinkage between thin and thick regions. The warpage of the flat part with a partly thick volume can be reduced by a proper design of the cooling system in the injection mould. The goal of this paper is to design properly cooling channels of injection mould to manufacture a flat part with a partly thick volume. The conformal cooling channel is adopted to improve cooling characteristics of a region with the thick volume. The linear cooling channels are assigned to the other region. The proper design of the conformal cooling channels is obtained from three-dimensional injection molding analysis for various design alternatives. The moulding characteristics of the designed mould with both conformal and linear cooling channels are compared to those of the mould with linear cooling channels from viewpoints of temperature, shrinkage and warpage of the moulded part using numerical analysis. Injection mould with both conformal and linear cooling channels for the flat part with a partially thick volume is fabricated. In addition, injection moulding experiments are performed using the fabricated mould. From the results of the injection moulding experiments, it has been shown that the designed mould can successfully fabricate the flat part with a partially thick volume.

• 대한수학회지
• /
• 제43권1호
• /
• pp.133-145
• /
• 2006

We study Riemannian or pseudo-Riemannian manifolds which admit a closed conformal vector field. Subject to the condition that at each point $p{\in}M^n$ the set of conformal gradient vector fields spans a non-degenerate subspace of TpM, using a warped product structure theorem we give a complete description of the space of conformal vector fields on arbitrary non-Ricci flat Einstein spaces.

• Kyungpook Mathematical Journal
• /
• 제51권1호
• /
• pp.109-124
• /
• 2011

The main objective of the paper is to provide a full classification of quasi-conformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.

• Kyungpook Mathematical Journal
• /
• 제61권4호
• /
• pp.781-790
• /
• 2021

The goal of this paper is to characterize a class of almost Kenmotsu manifolds admitting *-conformal Ricci solitons. It is shown that if a (2n + 1)-dimensional (k, µ)'-almost Kenmotsu manifold M admits *-conformal Ricci soliton, then the manifold M is *-Ricci flat and locally isometric to ℍⁿ⁺¹(-4) × ℝⁿ. The result is also verified by an example.

• 대한수학회논문집
• /
• 제35권1호
• /
• pp.269-278
• /
• 2020

This paper aims to study the geometrical properties of the conharmonic curvature tensor of a locally conformal almost cosymplectic manifold. The necessary and sufficient conditions for the conharmonic curvature tensor to be flat, the locally conformal almost cosymplectic manifold to be normal and an η-Einstein manifold were determined.

• 대한수학회논문집
• /
• 제36권1호
• /
• pp.165-171
• /
• 2021

The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton (Mn, g, f, λ) with constant scalar curvature admitting a non-homothetic conformal vector field V leaving the potential vector field invariant. We show that in such manifolds the potential function f is constant and the scalar curvature of g is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field V, without constant scalar curvature assumption, we show that g has constant curvature and determines the potential function f explicitly.