Some progress in conformal geometry.
Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Graham, Robin C.
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Let be the interior of a compact manifold of dimension with boundary , and be a conformally compact metric on , namely extends continuously (or with some degree of smoothness) as a metric to , where denotes a defining function for , i.e. on and , on . The restrction of to rescales upon changing , so defines invariantly a conformal class of metrics on , which is called the conformal infinity of . In the present paper, the author considers conformally compact...
Labbi, Mohammed Larbi (2010)
Balkan Journal of Geometry and its Applications (BJGA)
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Sharief Deshmukh, Falleh Al-Solamy (2008)
Colloquium Mathematicae
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It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold...
Sun-Yung A. Chang, Matthew J. Gursky, Paul C. Yang (2003)
Publications Mathématiques de l'IHÉS
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Hijazi, Oussama, Raulot, Simon (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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W. Roter (1982)
Colloquium Mathematicae
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Harish Seshadri (2010)
Annales de l’institut Fourier
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Let , , be a compact simply-connected Riemannian -manifold with nonnegative isotropic curvature. Given , we prove that there exists satisfying the following: If the scalar curvature of satisfies and the Einstein tensor satisfies then is diffeomorphic to a symmetric space of compact type. This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature. ...