Conformal deformation on a semi-Riemannian manifold (I)

Yoon-Tae Jung; Soo-Young Lee

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Bull. Korean Math. Soc. 2001; 38(2): 223-230

Printed June 1, 2001

Conformal deformation on a semi-Riemannian manifold (I)

Yoon-Tae Jung and Soo-Young Lee

Chosun University, Chosun University

Abstract

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Abstract

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

Keywords: conformal deformation, Lorentzian warped manifold, scalar curvature

MSC numbers: 53C21, 53C50, 58C35, 58J05