Affine analogues of the Sasaki-Shchepetilov connection
| Autor: | Maria Robaszewska |
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| Jazyk: | German<br />English<br />French |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, Vol 15, Pp 37-49 (2016) |
| Druh dokumentu: | article |
| ISSN: | 2081-545X 2300-133X |
| DOI: | 10.1515/aupcsm-2016-0004 |
| Popis: | For two-dimensional manifold M with locally symmetric connection ∇ and with ∇-parallel volume element vol one can construct a flat connection on the vector bundle TM⊕E, where E is a trivial bundle. The metrizable case, when M is a Riemannian manifold of constant curvature, together with its higher dimension generalizations, was studied by A.V. Shchepetilov [J. Phys. A: 36 (2003), 3893-3898]. This paper deals with the case of non-metrizable locally symmetric connection. Two flat connections on TM⊕(R⨯M) and two on TM⊕(R2⨯M) are constructed. It is shown that two of those connections - one from each pair - may be identified with the standard flat connection in RN, after suitable local affine embedding of (M,∇) into RN. |
| Databáze: | Directory of Open Access Journals |
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