THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES (II)

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 1,  2011, pp.121-127
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.1.121
Title & Authors
THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES (II)
Jung, Yoon-Tae;

Abstract
In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times $M Keywords warped product;scalar curvature;conformal deformation; Language English Cited by 1. The Nonexistence of Conformal Deformations on Riemannian Warped Product Manifolds, Journal of the Chosun Natural Science, 2012, 5, 1, 42 References 1. P. Aviles and R. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, Diff. Geom. 27(1988), 225-239. 2. J.K. Beem, P.E. Ehrlich and Th.G. Powell, Warped product manifolds in relativity, Selected Studies (Th.M. Rassias, G.M. Rassias, eds.), North-Holland, 1982, 41-56. 3. Y.T. Jung and S.C. Lee, The nonexistence of conformal deformations on space-times, Honam Math. J. 32(2010), 85-89. 4. J.L. Kazdan and F.W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J.Diff.Geo. 10(1975), 113-134. 5. J.L. Kazdan and F.W. Warner, Existence and conformal deformation of metrics with prescribed Guassian and scalar curvature, Ann. of Math. 101(1975), 317-331. 6. M.C.Leung, Conformal scalar curvature equations on complete manifolds, Comm. in P.D.E. 20 (1995), 367-417 7. M.C. Leung, Conformal deformation of warped products and scalar curvature functions on open manifolds, preprint. 8. M.C.Leung, Uniqueness of Positive Solutions of the Equation$\Delta_{g0}\;+\;c_nu\;=\;c_nu^{\frac{n+2}{n-2}}\$ and Applications to Conformal Transformations, preprint.

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