Honam Mathematical Journal (호남수학학술지)
- Volume 33 Issue 1
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- Pages.121-127
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- 2011
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- 1225-293X(pISSN)
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- 2288-6176(eISSN)
DOI QR Code
THE NONEXISTENCE OF CONFORMAL DEFORMATIONS ON SPACE-TIMES (II)
- Jung, Yoon-Tae (Department of Mathematics, Chosun University)
- Received : 2011.03.04
- Accepted : 2011.03.11
- Published : 2011.03.25
Abstract
In this paper, when N is a compact Riemannian manifold, we discuss the nonexistence of conformal deformations on space-times
Keywords
warped product;scalar curvature;conformal deformation
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References
- P. Aviles and R. McOwen, Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds, Diff. Geom. 27(1988), 225-239. https://doi.org/10.4310/jdg/1214441781
- 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.
- Y.T. Jung and S.C. Lee, The nonexistence of conformal deformations on space-times, Honam Math. J. 32(2010), 85-89. https://doi.org/10.5831/HMJ.2010.32.1.085
- J.L. Kazdan and F.W. Warner, Scalar curvature and conformal deformation of Riemannian structure, J.Diff.Geo. 10(1975), 113-134. https://doi.org/10.4310/jdg/1214432678
- 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. https://doi.org/10.2307/1970993
- M.C.Leung, Conformal scalar curvature equations on complete manifolds, Comm. in P.D.E. 20 (1995), 367-417 https://doi.org/10.1080/03605309508821100
- M.C. Leung, Conformal deformation of warped products and scalar curvature functions on open manifolds, preprint.
-
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. - D.S. Mitrinovic, Analytic inequalities, Springer-Verlag, New York Heidelberge Berlin, 1970
- A. Ratto, M. Rigoli and G. Setti, On the Omori-Yau maximum principle and its applications to differential equations and geometry, J. Functional Analysis 134(1995), 486-510. https://doi.org/10.1006/jfan.1995.1154
Cited by
- The Nonexistence of Conformal Deformations on Riemannian Warped Product Manifolds vol.5, pp.1, 2012, https://doi.org/10.13160/ricns.2012.5.1.042