منابع مشابه
Einstein Metrics , Four - Manifolds , and Differential Topology
where r is the Ricci tensor of g and λ is some real constant [7]. We still do not know if there are any obstructions to the existence of Einstein metrics on highdimensional manifolds, but it has now been known for three decades that not every 4-manifold admits such metrics [20, 37]. Only recently, however, has it emerged that there are also obstructions to the existence of Einstein metrics whic...
متن کاملSpin Manifolds, Einstein Metrics, and Differential Topology
We show that there exist smooth, simply connected, fourdimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy refinement of the Seiberg-Witten invariant [3, 9], in conjunction with curvature estimates previously proved by the second author [17]. These methods also all...
متن کاملWarped product and quasi-Einstein metrics
Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...
متن کاملEinstein Metrics , Four - Manifolds , and Differential Topology Claude
where r is the Ricci tensor of g and λ is some real constant [7]. We still do not know if there are any obstructions to the existence of Einstein metrics on highdimensional manifolds, but it has now been known for three decades that not every 4-manifold admits such metrics [20, 37]. Only recently, however, has it emerged that there are also obstructions to the existence of Einstein metrics whic...
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: Journal of Differential Geometry
سال: 1976
ISSN: 0022-040X
DOI: 10.4310/jdg/1214433423