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In this paper, we prove that a closed even-dimensional manifold which is locally conformally flat with positive scalar curvature, positive Euler characteristic and which satisfies some additional condition on its curvature is diffeomorphic to the sphere or projective space. 相似文献
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Marco Caldarelli Giovanni Catino Zindine Djadli Annibale Magni Carlo Mantegazza 《Geometriae Dedicata》2010,145(1):127-137
By means of a Kaluza–Klein type argument we show that the Perelman’s F{mathcal{F}} -functional is the Einstein–Hilbert action in a space with extra “phantom” dimensions. In this way, we try to interpret some remarks of Perelman in the introduction and at the end of the first section in his famous paper (Perelman in The entropy formula for the Ricci flow and its geometric applications, 2002). As a consequence the Ricci flow (modified by a diffeomorphism and a time-dependent factor) is the evolution of the “real” part of the metric under a constrained gradient flow of the Einstein–Hilbert gravitational action in higher dimension. 相似文献
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Zindine?DjadliEmail author Andrea?Malchiodi Ould?Ahmedou 《Journal of Geometric Analysis》2003,13(2):255-289
We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half-three sphere,
by deforming conformally its standard metric. Using blow-up analysis techniques and minimax arguments, we prove some existence
and compactness results. 相似文献
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Given a four-dimensional manifold , we study the existence of a conformal metric for which the Q-curvature, associated to a conformally invariant fourth-order operator (the Paneitz operator), is constant. Using a topological argument, we obtain a new result in cases which were still open. To cite this article: Z. Djadli, A. Malchiodi, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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