Spin(9) geometry of the octonionic Hopf fibration
Differential Geometry
2020-07-30 v2
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.
Keywords
Cite
@article{arxiv.1208.0899,
title = {Spin(9) geometry of the octonionic Hopf fibration},
author = {Liviu Ornea and Maurizio Parton and Paolo Piccinni and Victor Vuletescu},
journal= {arXiv preprint arXiv:1208.0899},
year = {2020}
}
Comments
Proofs and Examples revised, some references added