Spin(9) geometry of the octonionic Hopf fibration

Autor:	Paolo Piccinni, Victor Vuletescu, Liviu Ornea, Maurizio Parton
Rok vydání:	2013
Předmět:	Algebra and Number Theory Zero (complex analysis) Structure (category theory) Vector field Conformal map Geometry Geometry and Topology Algebra over a field Symmetry group Hopf fibration Mathematics Spin-½
Zdroj:	Transformation Groups. 18:845-864
ISSN:	1531-586X 1083-4362
DOI:	10.1007/s00031-013-9233-x
Popis:	We deal with Riemannian properties of the octonionic Hopf fibration S15 → S8, 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 S1 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e8ba591c9b0e841be7e1a7dca85d9243 https://doi.org/10.1007/s00031-013-9233-x Zobrazit plný text záznamu Full text from SpringerLink