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 / Liviu, Ornea; Maurizio, Parton; Piccinni, Paolo; Vuletescu, Victor. - In: TRANSFORMATION GROUPS. - ISSN 1083-4362. - STAMPA. - 18:3(2013), pp. 845-864. [10.1007/s00031-013-9233-x]
SPIN(9) GEOMETRY OF THE OCTONIONIC HOPF FIBRATION
PICCINNI, Paolo;
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
