A classification of locally homogeneous connections on 2-dimensional manifolds via group-theoretical approach

• Autorzy: Oldřich Kowalski , Barbara Opozda , Zdeněk Vlášek
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to classify (lócally) all torsion-less locally homogeneous affine connections on two-dimensional manifolds from a group-theoretical point of view. For this purpose, we are using the classification of all non-equivalent transitive Lie algebras of vector fields in ℝ2 according to P.J. Olver [7].

Słowa kluczowe

EN

Two-dimensional manifolds with affine connection; locally homogeneous connections; Lie algebras of vector fields; Killing vector fields; 53B05; 53C30

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 1
• Strony: 87-102

Daty

wydano

2004-03-01

online

2004-03-01

Twórcy

autor

Oldřich Kowalski

• Charles University

autor

Barbara Opozda

• Jagiellonian University

autor

Zdeněk Vlášek

• Charles University

Bibliografia

• [1] S. Kobayashi: Transformation Groups in Differential Geometry, Springer-Verlag, New York, 1972.
• [2] S. Kobayashi, K. Nomizu: Foundations of Differential Geometry I, Interscience Publ., New York, 1963.
• [3] O. Kowalski, B. Opozda, Z. Vlášek: “Curvature homogeneity of affine connections on two-dimensional manifolds”, Colloquium Mathematicum, Vol. 81, (1999), pp. 123–139.
• [4] O. Kowalski, B. Opozda, Z. Vlášek: “A classification of locally homogeneous affine connections with skew-symmetric Ricci tensor on 2-dimensional manifolds”, Monatshefte für Mathematik, (2000), pp. 109–125.
• [5] O. Kowalski, Z. Vlášek: “On the local moduli space of locally homogeneous affine connections in plane domains”, Comment. Math. Univ. Carolinae, (2003), pp. 229–234.
• [6] K. Nomizu, T. Sasaki: Affine Differential Geometry, Cambridge University Press, Cambridge, 1994.
• [7] P.J. Olver: Equivalence, Invariants and Symmetry Cambridge University Press, Cambridge, 1995.
• [8] B. Opozda: “Classification of locally homogeneous connections on 2-dimensional manifolds”, to appear in Diff. Geom. Appl..

Identyfikatory

DOI

10.2478/BF02475953