منابع مشابه
Einstein Metrics on Spheres
Any sphere S admits a metric of constant sectional curvature. These canonical metrics are homogeneous and Einstein, that is the Ricci curvature is a constant multiple of the metric. The spheres S, m > 1 are known to have another Sp(m + 1)-homogeneous Einstein metric discovered by Jensen [Jen73]. In addition, S has a third Spin(9)-invariant homogeneous Einstein metric discovered by Bourguignon a...
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We give an elementary treatment of the existence of complete Kähler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n + 1)-sphere. Mathematics Subject Classification (2000) 53C
متن کاملSasakian Geometry and Einstein Metrics on Spheres
This paper is based on a talk presented by the first author at the Short Program on Riemannian Geometry that took place at the Centre de Recherche Mathématiques, Université de Montréal, during the period June 28-July 16, 2004. It is a report on our joint work with János Kollár [BGK03] concerning the existence of an abundance of Einstein metrics on odd dimensional spheres, including exotic spher...
متن کاملEinstein Metrics on Rational Homology Spheres
In this paper we prove the existence of Einstein metrics, actually SasakianEinstein metrics, on nontrivial rational homology spheres in all odd dimensions greater than 3. It appears as though little is known about the existence of Einstein metrics on rational homology spheres, and the known ones are typically homogeneous. The are two exception known to the authors. Both involve Sasakian geometr...
متن کاملon einstein (α,β )-metrics
– in this paper we consider some (α ,β ) -metrics such as generalized kropina, matsumoto and f (α β )2α = + metrics, and obtain necessary and sufficient conditions for them to be einstein metrics when βis a constant killing form. then we prove with this assumption that the mentioned einstein metrics must beriemannian or ricci flat.
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2005
ISSN: 0003-486X
DOI: 10.4007/annals.2005.162.557