• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.865-879
• /
• 2022

Let (M^m, g) be an m-dimensional Riemannian manifold. In this paper, we introduce a new class of metric on (M^m, g), obtained by a non-conformal deformation of the metric g. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. In the last section we characterizes some class of proper biharmonic maps. Examples of proper biharmonic maps are constructed when (M^m, g) is an Euclidean space.

• Honam Mathematical Journal
• /
• v.33 no.1
• /
• pp.121-127
• /
• 2011

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times $M = (a,\infty){\times}_fN$ with prescribed scalar curvature functions.

• Honam Mathematical Journal
• /
• v.32 no.1
• /
• pp.85-89
• /
• 2010

In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times M = $({\alpha},{\infty}){\times}_fN$ with prescribed scalar curvature functions.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.133-140
• /
• 2002

On compact complex hyperbolic manifolds of complex dimension two, we show that the dimension of the space of infinitesimal deformations of self-dual conformal structures is smaller than that of the deformation obstruction space and that every self-dual metric with covariantly constant Ricci tensor must be a standard one upto rescalings and diffeomorphisms.

• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.223-230
• /
• 2001

In this parper, we considered the uniqueness of positive time-solution to equation ${\Box}_g$u(t,$\chi$) - $c_n$u(t,$\chi$) + $c_n$u(t,$\chi$)$^[\frac{n+3}{n-3}]$ = 0, where $c_n$ = $\frac{n-1}{4n}$ and ${\Box}_g$ is the d'Alembertian for a Lorentzian warped manifold M = {a,$\infty$] $\times_f$ N.

• The Pure and Applied Mathematics
• /
• v.4 no.1
• /
• pp.27-33
• /
• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.

• The Pure and Applied Mathematics
• /
• v.10 no.2
• /
• pp.119-126
• /
• 2003

In this paper, when N is a compact Riemannian manifold, we considered the positive time solution to equation $\Box_gu(t,x)-c_nu(t,x)+c_nu(t,x)^{(n+3)/(n-1)}$ on M ＝$(-{\infty},+{\infty})\;{\times}_f\;N$, where $c_n$ ＝(n－1)/4n and $\Box_{g}$ is the d'Alembertian for a Lorentzian warped manifold.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.205-214
• /
• 2016

Any open Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we will prove that, given any open Riemann surface, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. This result along with [5] now shows that an open Riemann surface admits conformal models in any Riemannian manifold of dimension ${\geq}3$.

• Bulletin of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.133-142
• /
• 1990

In this paper, we define a new tensor field on a Sasqakian manifold, which is constructed from the conformal curvature tensor field by using the Boothby-Wang's fibration ([3]), and study some properties of this new tensor field. In Section 2, we recall definitions and fundamental properties of Sasakian manifold and .phi.-holomorphic sectional curvature. In Section 3, we define contact conformal curvature tensor field on a Sasakian manifold and prove that it is invariant under D-homothetic deformation due to S. Tanno([13]). In Section 4, we study Sasakian manifolds with vanishing contact conformal curvature tensor field, and the last Section 5 is devoted to studying some properties of fibred Riemannian spaces with Sasakian structure of vanishing contact conformal curvature tensor field.

• The Mathematical Education
• /
• v.33 no.1
• /
• pp.123-128
• /
• 1994