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Sasakian manifold

About: Sasakian manifold is a research topic. Over the lifetime, 589 publications have been published within this topic receiving 6268 citations.


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01 Jan 1976
TL;DR: In this paper, the tangent sphere bundle is shown to be a contact manifold, and the contact condition is interpreted in terms of contact condition and k-contact and sasakian structures.
Abstract: Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metric structures.- The tangent sphere bundle.

1,259 citations

Journal ArticleDOI
TL;DR: A nearly parallel G 2 -structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor as discussed by the authors, and the automorphism group of such structures is defined.

267 citations

Journal ArticleDOI
TL;DR: In this paper, the authors define and study both bi-slant and semisupermanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold.
Abstract: We define and study both bi-slant and semi-slant submanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold We prove a characterization theorem for semi-slant submanifolds and we obtain integrability conditions for the distributions which are involved in the definition of such submanifolds We also study an interesting particular class of semi-slant submanifolds

189 citations

Journal ArticleDOI
TL;DR: In this paper, candidate superconformal N = 2 gauge theories that realize the AdS/CFT correspondence with M-theory compactified on the homogeneous Sasakian 7 -manifolds M 7 were classified long ago.

188 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied η-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds and used a previous solution of the Calabi problem in the context of Sasakian geometry to prove the existence of ηEinstein structures on many different compact manifolds including exotic spheres.
Abstract: A compact quasi-regular Sasakian manifold M is foliated by one-dimensional leaves and the transverse space of this characteristic foliation is necessarily a compact Kahler orbifold . In the case when the transverse space is also Einstein the corresponding Sasakian manifold M is said to be Sasakian η-Einstein. In this article we study η-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem in the context of Sasakian geometry to prove the existence of η-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl and Lorenzian Sasakian-Einstein structures.

159 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20221
202132
202032
201930
201830
201732