dorsal/arxiv
View SchemaHomogeneous phase spaces: the Cayley-Klein framework
| Authors | Francisco J. Herranz, Mariano Santander |
|---|---|
| Categories | |
| ArXiv ID | physics/9702030 |
| URL | https://arxiv.org/abs/physics/9702030 |
| Journal | Geometria y Fisica, Eds: J.F. Cari\~nena, E. Martinez, M.F. Ra\~nada, Memorias de la Real Academia de Ciencias, Madrid, vol. XXXII, 1998, pp. 59-84 |
Abstract
The metric structure of homogeneous spaces of rank-one and rank-two associated to the real pseudo-orthogonal groups SO(p,q) and some of their contractions (e.g., ISO(p,q), Newton-Hooke type groups...) is studied. All these spaces are described from a unified setting following a Cayley-Klein scheme allowing to simultaneously study the main features of their Riemannian, pesudoRiemannian and semiRiemannian metrics, as well as of their curvatures. Some of the rank-one spaces are naturally interpreted as spacetime models. Likewise, the same natural interpretation for rank-two spaces is as spaces of lines in rank-one spaces; through this relation these rank-two spaces give rise to homogeneous phase space models. The main features of the phase spaces for homogeneous spacetimes are analysed.
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"abstract": "The metric structure of homogeneous spaces of rank-one and rank-two\nassociated to the real pseudo-orthogonal groups SO(p,q) and some of their\ncontractions (e.g., ISO(p,q), Newton-Hooke type groups...) is studied. All\nthese spaces are described from a unified setting following a Cayley-Klein\nscheme allowing to simultaneously study the main features of their Riemannian,\npesudoRiemannian and semiRiemannian metrics, as well as of their curvatures.\nSome of the rank-one spaces are naturally interpreted as spacetime models.\nLikewise, the same natural interpretation for rank-two spaces is as spaces of\nlines in rank-one spaces; through this relation these rank-two spaces give rise\nto homogeneous phase space models. The main features of the phase spaces for\nhomogeneous spacetimes are analysed.",
"arxiv_id": "physics/9702030",
"authors": [
"Francisco J. Herranz",
"Mariano Santander"
],
"categories": [
"math-ph",
"math.MP"
],
"journal_ref": "Geometria y Fisica, Eds: J.F. Cari\\~nena, E. Martinez, M.F.\n Ra\\~nada, Memorias de la Real Academia de Ciencias, Madrid, vol. XXXII, 1998,\n pp. 59-84",
"title": "Homogeneous phase spaces: the Cayley-Klein framework",
"url": "https://arxiv.org/abs/physics/9702030"
},
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