Open Access
January, 2017 Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds
Craig van COEVERING
J. Math. Soc. Japan 69(1): 53-91 (January, 2017). DOI: 10.2969/jmsj/06910053

Abstract

We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations preserving 2, 1, or none of the 3 independent Killing spinors. Toric 3-Sasakian manifolds provide non-trivial examples with integrable deformation preserving precisely 2 Killing spinors. Thus in contrast to the case of parallel spinors the dimension of Killing spinors is not preserved under Einstein deformations but is only upper semi-continuous.

Citation

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Craig van COEVERING. "Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds." J. Math. Soc. Japan 69 (1) 53 - 91, January, 2017. https://doi.org/10.2969/jmsj/06910053

Information

Published: January, 2017
First available in Project Euclid: 18 January 2017

zbMATH: 1373.53066
MathSciNet: MR3597547
Digital Object Identifier: 10.2969/jmsj/06910053

Subjects:
Primary: 53C25
Secondary: 32Q20

Keywords: 3-Sasakian , Einstein deformation , Killing spinor , Sasaki–Einstein

Rights: Copyright © 2017 Mathematical Society of Japan

Vol.69 • No. 1 • January, 2017
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