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Spin(9) geometry of the octonionic Hopf fibration

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Abstract

We deal with Riemannian properties of the octonionic Hopf fibration S 15 → S 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.

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Author information

Authors and Affiliations

  1. University of Bucharest, Faculty of Mathematics and Informatics, 14 Academiei str., 70109, Bucharest, Romania

    Liviu Ornea & Victor Vuletescu

  2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Str., 010702, Bucharest, Romania

    Liviu Ornea

  3. Università di Chieti-Pescara, Dipartimento di Economia, Viale Pindaro 87, I-65127, Pescara, Italy

    Maurizio Parton

  4. Dipartimento di Matematica, Sapienza—Università di Roma, Piazzale Aldo Moro 2, I-00185, Roma, Italy

    Paolo Piccinni

Authors
  1. Liviu Ornea
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  2. Maurizio Parton
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  3. Paolo Piccinni
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  4. Victor Vuletescu
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Corresponding author

Correspondence to Liviu Ornea.

Additional information

L. O. and V. V. were partially supported by CNCS UEFISCDI, project number PNII-ID-PCE-2011-3-0118 and by the INdAM-GNSAGA visiting program.

M. P. and P. P. were supported by the MIUR under the 2010–11 PRIN Project “Varietà reali e complesse: geometria, topologia e analisi armonica”.

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Ornea, L., Parton, M., Piccinni, P. et al. Spin(9) geometry of the octonionic Hopf fibration. Transformation Groups 18, 845–864 (2013). https://doi.org/10.1007/s00031-013-9233-x

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  • DOI: https://doi.org/10.1007/s00031-013-9233-x

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