The Role of Spin(9) in Octonionic Geometry†
Dipartimento di Economia, Università di Chieti-Pescara, Viale della Pineta 4, I-65129 Pescara, Italy;
Dipartimento di Matematica, Sapienza—Università di Roma, Piazzale Aldo Moro 2, I-00185 Roma, Italy
This paper is dedicated to the memory of Thomas Friedrich.
Author to whom correspondence should be addressed.
Received: 20 September 2018 / Revised: 4 October 2018 / Accepted: 6 October 2018 / Published: 12 October 2018
Starting from the 2001 Thomas Friedrich’s work on
, we review some interactions between
and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the
canonical 8-form and its analogies with quaternionic geometry as well as the role of
both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel
manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley–Rosenfeld planes and to three series of Grassmannians.
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MDPI and ACS Style
Parton, M.; Piccinni, P. The Role of Spin(9) in Octonionic Geometry. Axioms 2018, 7, 72.
Parton M, Piccinni P. The Role of Spin(9) in Octonionic Geometry. Axioms. 2018; 7(4):72.
Parton, Maurizio; Piccinni, Paolo. 2018. "The Role of Spin(9) in Octonionic Geometry." Axioms 7, no. 4: 72.
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