1,965 research outputs found
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
Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics
We review our study of Sasakian geometry as an agent for proving the
existence of Einstein metrics on odd dimensional manifolds. Particular emphasis
is given to the Sasakian structures occuring on links of isolated hypersurface
singularities.Comment: This is an expository article that grew out of notes for the three
lectures the second author presented during the XXIV-th Winter School of {\it
Geometry and Physics} in Srni, Czech Republic, in January of 2004., 30 pages.
Some new examples and references were adde
Rational Homology 5-Spheres with Positive Ricci Curvature
We prove that for every integer k>1 there is a simply connected rational
homology 5-sphere with spin such that
\scriptstyle{H_2(M^5_k,\bbz)} has order and
admits a Riemannian metric of positive Ricci curvature.
Moreover, if the prime number decomposition of has the form
for distinct primes then
is uniquely determined.Comment: 8 page
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