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.

Spin(9) geometry of the octonionic Hopf fibration

PARTON, Maurizio
;
2013

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11564/480886
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