- Tytuł:
- Affine analogues of the Sasaki-Shchepetilov connection
- Autorzy:
- Robaszewska, Maria
- Powiązania:
- https://bibliotekanauki.pl/articles/744685.pdf
- Data publikacji:
- 2016-12-01
- Wydawca:
- Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
- Tematy:
-
connection on a vector bundle
associated vector bundle
connection form
locally symmetric connection - Opis:
- 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.
- Źródło:
-
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2016, 15
2300-133X - Pojawia się w:
- Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł