Sasakian Geometry, Holonomy, and Supersymmetry

Details Sasakian Geometry, Holonomy, and Supersymmetry Sasakian Geometry, Holonomy, and Supersymmetry

2007-03-08

arxiv.org/abs/math/0703231v2

Mathematics

Differential Geometry

40 pages, some minor corrections made, to appear in the Handbook of pseudo-Riemannian Geometry and Supersymmetry

Scientific paper

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.

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