Geodesic
On some flat connection associated with locally symmetric surface
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014).

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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. 
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Robaszewska, Maria. On some flat connection associated with locally symmetric surface. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 13 (2014). http://geodesic.mathdoc.fr/item/AUPCM_2014_13_a4/

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