Institute for Mathematical Physics Einstein Manifolds and Contact Geometry Einstein Manifolds and Contact Geometry
نویسندگان
چکیده
We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.
منابع مشابه
Conformal mappings preserving the Einstein tensor of Weyl manifolds
In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...
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 کاملNotes on some classes of 3-dimensional contact metric manifolds
A review of the geometry of 3-dimensional contact metric manifolds shows that generalized Sasakian manifolds and η-Einstein manifolds are deeply interrelated. For example, it is known that a 3-dimensional Sasakian manifold is η-Einstein. In this paper, we discuss the relationships between several special classes of 3-dimensional contact metric manifolds which are generalizations of 3-dimensiona...
متن کاملEinstein Manifolds and Contact Geometry
We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.
متن کاملSasakian Geometry, Hypersurface Singularities, and Einstein Metrics Charles P. Boyer and Krzysztof Galicki
This review article has grown out of notes for the three lectures the second author presented during the XXIV-th Winter School of Geometry and Physics in Srni, Czech Republic, in January of 2004. Our purpose is twofold. We want give a brief introduction to some of the techniques we have developed over the last 5 years while, at the same time, we summarize all the known results. We do not give a...
متن کامل