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Spin(9) geometry of the octonionic Hopf fibration |
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| Authors: | Liviu Ornea Maurizio Parton Paolo Piccinni Victor Vuletescu |
| Institution: | 1. University of Bucharest, Faculty of Mathematics and Informatics, 14 Academiei str., 70109, Bucharest, Romania 2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Str., 010702, Bucharest, Romania 3. Università di Chieti-Pescara, Dipartimento di Economia, Viale Pindaro 87, I-65127, Pescara, Italy 4. Dipartimento di Matematica, Sapienza—Università di Roma, Piazzale Aldo Moro 2, I-00185, Roma, Italy |
| 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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