Deformations of Killing spinors on Sasakian and 3-Sasakian manifolds

VAN COEVERING C. C.

Journal of the Mathematical Society of Japan, cilt.69, sa.1, ss.53-91, 2017 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 1
  • Basım Tarihi: 2017
  • Doi Numarası: 10.2969/jmsj/06910053
  • Dergi Adı: Journal of the Mathematical Society of Japan
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.53-91
  • Anahtar Kelimeler: 3-Sasakian, Einstein deformation, Killing spinor, Sasaki-Einstein
  • Boğaziçi Üniversitesi Adresli: Evet

Özet

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.