Journal of the Mathematical Society of Japan

Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds


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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.

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J. Math. Soc. Japan, Volume 69, Number 1 (2017), 53-91.

First available in Project Euclid: 18 January 2017

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Zentralblatt MATH identifier

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx]

Killing spinor Sasaki–Einstein 3-Sasakian Einstein deformation


van COEVERING, Craig. Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds. J. Math. Soc. Japan 69 (2017), no. 1, 53--91. doi:10.2969/jmsj/06910053.

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