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Ricci curvature of conformal deformation on compact 2-manifolds
Department of Mathematics, Chosun University, Kwangju, 61452, Republic of Korea |
In this paper, we consider Ricci curvature of conformal deformation on compact 2-manifolds. And we prove that, by the conformal deformation, the resulting manifold is an Einstein manifold.
References:
| [1] |
T. Aubin, Nonlinear Analysis on Manifolds, Springer-Verlag, New York, 1982. |
| [2] |
M. S. Berger,
Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Differ. Geom., 5 (1971), 325-332.
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| [3] |
A. L. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987.
doi: 10.1007/978-3-540-74311-8. |
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H. Ge and W. Jiang,
Kazdan-Warner equation on infinite graph, J. Korean Math. Soc., 55 (2018), 1091-1101.
doi: 10.4134/JKMS.j170561. |
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J. L. Kazdan and F. W. Warner,
Curvature functions for compact 2-manifolds, Ann. Math., 99 (1974), 14-47.
doi: 10.2307/1971012. |
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B. O'Neill, Semi-Riemannian Geometry, Academic, New York, 1983. |
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R. Walter, Real and Complex Analysis, McGraw-Hill, Singapore, 1986. Google Scholar |
show all references
References:
| [1] |
T. Aubin, Nonlinear Analysis on Manifolds, Springer-Verlag, New York, 1982. |
| [2] |
M. S. Berger,
Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Differ. Geom., 5 (1971), 325-332.
|
| [3] |
A. L. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987.
doi: 10.1007/978-3-540-74311-8. |
| [4] |
H. Ge and W. Jiang,
Kazdan-Warner equation on infinite graph, J. Korean Math. Soc., 55 (2018), 1091-1101.
doi: 10.4134/JKMS.j170561. |
| [5] |
J. L. Kazdan and F. W. Warner,
Curvature functions for compact 2-manifolds, Ann. Math., 99 (1974), 14-47.
doi: 10.2307/1971012. |
| [6] |
B. O'Neill, Semi-Riemannian Geometry, Academic, New York, 1983. |
| [7] |
R. Walter, Real and Complex Analysis, McGraw-Hill, Singapore, 1986. Google Scholar |
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