For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on some principal fibre bundle P(M,G). Associated with - satisfying some particular conditions - local basis of TM local connection form of such a connection is an R(G)-valued 1-form build from the dual basis ω1, ω2 and from the local connection form ω of ▽. The structural equations of (M,∇) are equivalent to the condition dΩ-Ω∧Ω=0. This work was intended as an attempt to describe in a unified way the construction of similar 1-forms known for constant Gauss curvature surfaces, in particular of that given by R. Sasaki for pseudospherical surfaces.
@article{bwmeta1.element.doi-10_2478_aupcsm-2014-0003,
author = {Maria Robaszewska},
title = {On some flat connection associated with locally symmetric surface},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
volume = {13},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_aupcsm-2014-0003}
}
Maria Robaszewska. On some flat connection associated with locally symmetric surface. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 13 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_aupcsm-2014-0003/
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