Annals of Global Analysis and Geometry

, Volume 46, Issue 2, pp 129–143 | Cite as

Generalized Killing spinors on spheres

  • Andrei MoroianuEmail author
  • Uwe Semmelmann


We study generalized Killing spinors on round spheres \(\mathbb {S}^n\). We show that on the standard sphere \(\mathbb {S}^8\) any generalized Killing spinor has to be an ordinary Killing spinor. Moreover, we classify generalized Killing spinors on \(\mathbb {S}^n\) whose associated symmetric endomorphism has at most two eigenvalues and recover in particular Agricola–Friedrich’s canonical spinor on 3-Sasakian manifolds of dimension 7. Finally, we show that it is not possible to deform Killing spinors on standard spheres into genuine generalized Killing spinors.


Generalized Killing spinors Parallel spinors 

Mathematics Subject Classification (2010)

Primary: 53C25 53C27 53C40 


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Versailles-St Quentin, UMR 8100 du CNRSVersaillesFrance
  2. 2.Fachbereich Mathematik, Institut für Geometrie und TopologieUniversität StuttgartStuttgartGermany

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