THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES

• Journal title : Honam Mathematical Journal
• Volume 32, Issue 1,  2010, pp.85-89
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2010.32.1.085
Title & Authors
THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES
Jung, Yoon-Tae; Lee, Sang-Cheol;

Abstract
In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times M = $\small{({\alpha},{\infty}){\times}_fN}$ with prescribed scalar curvature functions.
Keywords
warped product;scalar curvature;conformal deformation;
Language
English
Cited by
1.
THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES (II),;

호남수학학술지, 2011. vol.33. 1, pp.121-127
1.
The Nonexistence of Conformal Deformations on Riemannian Warped Product Manifolds, Journal of the Chosun Natural Science, 2012, 5, 1, 42
2.
THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES (II), Honam Mathematical Journal, 2011, 33, 1, 121
3.
SPHERICAL NEWTON DISTANCE FOR OSCILLATORY INTEGRALS WITH HOMOGENEOUS PHASE FUNCTIONS, Honam Mathematical Journal, 2011, 33, 1, 1
References
1.
P. Aviles and R. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, Diff. Geom. 27 (1988), 225-239.

2.
J.K. Seem, P.E. Ehrlich and Th.C. Powell, Warped product manifolds in relativity, Selected Studies (Th.M. Rassias, C.M. Rassias, eds.), North-Holland, 1982, 41-56.

3.
J.L. Kazdan and F.W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J.Diff.Geo. 10(1975), 113-134.

4.
J,L. Kazdan and F.W. Warner, Existence and conformal deformation of metrics with prescribed Guassian and scalar curvature, Ann. of Math. 101(1975), 317-331.

5.
M.C. Leung, Conformal scalar curvature equations on complete manifolds, Comm. in P.D.E. 20 (1995), 367-417

6.
M,C. Leung, Conformal deformation of warped products and scalar curvature functions on open manifolds, preprint.

7.
M.C.Leung, Uniqueness of Positive Solutions of the Equation $\Delta_{g0}$+$c_nu$ =$$c_nu^{\frac{n+2}{n-2}}$$ and Applications to Conformal Transformations, preprint.

8.
A. Ratto, M, Rigoli and C. Setti, On the Omori-Yau maximum principle and its applications to differential equations and geometry, J. Functional Analysis 134(1995), 486-510.