• 대한수학회논문집
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• 제37권3호
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• pp.865-879
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• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권2호
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• pp.119-126
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• 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.