18,147 research outputs found
On Sasaki-Einstein manifolds in dimension five
We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde
Contact Structures of Sasaki Type and their Associated Moduli
This article is based on a talk at the RIEMain in Contact conference in
Cagliari, Italy in honor of the 78th birthday of David Blair one of the
founders of modern Riemannian contact geometry. The present article is a survey
of a special type of Riemannian contact structure known as Sasakian geometry.
An ultimate goal of this survey is to understand the moduli of classes of
Sasakian structures as well as the moduli of extremal and constant scalar
curvature Sasaki metrics, and in particular the moduli of Sasaki-Einstein
metrics.Comment: 48 page
Highly connected manifolds with positive Ricci curvature
We prove the existence of Sasakian metrics with positive Ricci curvature on
certain highly connected odd dimensional manifolds. In particular, we show that
manifolds homeomorphic to the 2k-fold connected sum of S^{2n-1} x S^{2n} admit
Sasakian metrics with positive Ricci curvature for all k. Furthermore, a
formula for computing the diffeomorphism types is given and tables are
presented for dimensions 7 and 11.Comment: This is the version published by Geometry & Topology on 29 November
200
Sasakian Geometry, Holonomy, and Supersymmetry
In this expository article we discuss the relations between Sasakian
geometry, reduced holonomy and supersymmetry. It is well known that the
Riemannian manifolds other than the round spheres that admit real Killing
spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly
parallel G2 structure, and nearly Kaehler 6-manifolds. We then discuss the
relations between the latter two and Sasaki-Einstein geometry.Comment: 40 pages, some minor corrections made, to appear in the Handbook of
pseudo-Riemannian Geometry and Supersymmetr
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