Transformation Groups

, Volume 18, Issue 3, pp 845–864 | Cite as

Spin(9) geometry of the octonionic Hopf fibration

  • Liviu Ornea
  • Maurizio Parton
  • Paolo Piccinni
  • Victor Vuletescu


We deal with Riemannian properties of the octonionic Hopf fibration S 15S 8, in terms of the structure given by its symmetry group Spin(9). In particular, we show that any vertical vector field has at least one zero, thus reproving the non-existence of S 1 subfibrations. We then discuss Spin(9)-structures from a conformal viewpoint and determine the structure of compact locally conformally parallel Spin(9)-manifolds. Eventually, we give a list of examples of locally conformally parallel Spin(9)-manifolds.


Conformal Class Vectorial Type Vertical Vector Parallel Spin Vector Bundle Versus 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Liviu Ornea
    • 1
    • 2
  • Maurizio Parton
    • 3
  • Paolo Piccinni
    • 4
  • Victor Vuletescu
    • 1
  1. 1.University of Bucharest, Faculty of Mathematics and InformaticsBucharestRomania
  2. 2.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  3. 3.Università di Chieti-Pescara, Dipartimento di EconomiaPescaraItaly
  4. 4.Dipartimento di MatematicaSapienza—Università di RomaRomaItaly

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