The Role of Spin(9) in Octonionic Geometry
Starting from the 2001 Thomas Friedrich’s work on Spin ( 9 ) , we review some interactions between Spin ( 9 ) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin ( 9 ) canonical 8-form and its analogies with quat...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Axioms |
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| Online Access: | http://www.mdpi.com/2075-1680/7/4/72 |
| _version_ | 1818384615854833664 |
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| author | Maurizio Parton Paolo Piccinni |
| author_facet | Maurizio Parton Paolo Piccinni |
| author_sort | Maurizio Parton |
| collection | DOAJ |
| description | Starting from the 2001 Thomas Friedrich’s work on Spin ( 9 ) , we review some interactions between Spin ( 9 ) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin ( 9 ) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin ( 9 ) 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 Spin ( 9 ) 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. |
| first_indexed | 2024-12-14T03:25:05Z |
| format | Article |
| id | doaj.art-8d84f5f764514dc7ba56d8434f7ca1e1 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-12-14T03:25:05Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-8d84f5f764514dc7ba56d8434f7ca1e12022-12-21T23:18:54ZengMDPI AGAxioms2075-16802018-10-01747210.3390/axioms7040072axioms7040072The Role of Spin(9) in Octonionic GeometryMaurizio Parton0Paolo Piccinni1Dipartimento 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, ItalyStarting from the 2001 Thomas Friedrich’s work on Spin ( 9 ) , we review some interactions between Spin ( 9 ) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin ( 9 ) canonical 8-form and its analogies with quaternionic geometry as well as the role of Spin ( 9 ) 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 Spin ( 9 ) 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.http://www.mdpi.com/2075-1680/7/4/72Spin(9)octonionsvector fields on spheresHopf fibrationlocally conformally parallelClifford structureClifford systemsymmetric spaces |
| spellingShingle | Maurizio Parton Paolo Piccinni The Role of Spin(9) in Octonionic Geometry Axioms Spin(9) octonions vector fields on spheres Hopf fibration locally conformally parallel Clifford structure Clifford system symmetric spaces |
| title | The Role of Spin(9) in Octonionic Geometry |
| title_full | The Role of Spin(9) in Octonionic Geometry |
| title_fullStr | The Role of Spin(9) in Octonionic Geometry |
| title_full_unstemmed | The Role of Spin(9) in Octonionic Geometry |
| title_short | The Role of Spin(9) in Octonionic Geometry |
| title_sort | role of spin 9 in octonionic geometry |
| topic | Spin(9) octonions vector fields on spheres Hopf fibration locally conformally parallel Clifford structure Clifford system symmetric spaces |
| url | http://www.mdpi.com/2075-1680/7/4/72 |
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