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The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3223–3277 | Cite as

Spinorially Twisted Spin Structures, III: CR Structures

  • Rafael HerreraEmail author
  • Roger Nakad
  • Iván Téllez
Article
  • 97 Downloads

Abstract

We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin\(^{c, r}\) structure carrying a partially pure spinor field. We study various integrability conditions of the almost CR structure in our spinorial setup, including the classical integrability of a CR structure as well as those implied by Killing-type conditions on the partially pure spinor field. In the codimension one case, we develop a spinorial description of strictly pseudoconvex CR manifolds, metric contact manifolds, and Sasakian manifolds. Finally, we study hypersurfaces of Kähler manifolds via partially pure Spin\(^c\) spinors.

Keywords

Twisted spin structure Partially pure spinor Twisted Dirac operator CR structure 

Mathematics Subject Classification

53C10 53C25 53C27 58J50 58J60 32V05 

Notes

Acknowledgements

The authors are grateful to Oussama Hijazi for his encouragement and valuable comments. The authors thank Helga Baum and the Institute of Mathematics of the University of Humboldt-Berlin for their hospitality and support. The first author would also like to thank the hospitality and support of the International Centre for Theoretical Physics and the Institut des Hautes Études Scientifiques. The second author gratefully acknowledges the support and hospitality of the Centro de Investigación en Matemáticas A.C. (CIMAT). Rafael Herrera was partially supported by grants of CONACyT, LAISLA (CONACyT-CNRS), and the IMU Berlin Einstein Foundation Program. Iván Téllez was supported by a CONACyT scholarship.

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Copyright information

© Mathematica Josephina, Inc. 2017

Authors and Affiliations

  1. 1.Centro de Investigación en MatemáticasGuanajuatoMexico
  2. 2.Department of Mathematics and Statistics, Faculty of Natural and Applied SciencesNotre Dame University-LouaizéZouk MikaelLebanon

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