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Ricci curvature of conformal deformation on compact 2-manifolds

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The first author was supported by Chosun University Research Fund 2018

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  • 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.

    Mathematics Subject Classification: Primary: 53C21, 58E30; Secondary: 53C25.58H15, 58J05.


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  • [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.
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