Mathematische Annalen

, Volume 357, Issue 4, pp 1205–1216

Homogeneous almost quaternion-Hermitian manifolds

Article

DOI: 10.1007/s00208-013-0934-1

Cite this article as:
Moroianu, A., Pilca, M. & Semmelmann, U. Math. Ann. (2013) 357: 1205. doi:10.1007/s00208-013-0934-1

Abstract

An almost quaternion-Hermitian structure on a Riemannian manifold \((M^{4n},g)\) is a reduction of the structure group of \(M\) to \(\mathrm{Sp}(n)\mathrm{Sp}(1)\subset \text{ SO }(4n)\). In this paper we show that a compact simply connected homogeneous almost quaternion-Hermitian manifold of non-vanishing Euler characteristic is either a Wolf space, or \(\mathbb{S }^2\times \mathbb{S }^2\), or the complex quadric \(\text{ SO }(7)/\mathrm{U}(3)\).

Mathematics Subject Classification (2010)

Primary 53C30 53C35 53C15 Secondary 17B22 

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrei Moroianu
    • 1
  • Mihaela Pilca
    • 2
    • 3
  • Uwe Semmelmann
    • 4
  1. 1.Laboratoire de MathématiquesUniversité de Versailles-St QuentinVersaillesFrance
  2. 2.Fakultät für MathematikUniversität RegensburgRegensburgGermany
  3. 3.Institute of Mathematics“Simion Stoilow” of the Romanian AcademyBucharestRomania
  4. 4.Institut für Geometrie und Topologie, Fachbereich MathematikUniversität StuttgartStuttgartGermany