<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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. </p>
<p>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. </p>
</abstract>

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.

On some flat connection associated with locally symmetric surface

Institute of Mathematics Pedagogical University Podchorazych 2 30-084 Kraków Poland

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"On some flat connection associated with locally symmetric surface"}

For every two-dimensional manifold M with locally symmetric linear connection ∇, endowed also with ∇-parallel volume element, we construct a flat connection on...

On some flat connection associated with locally symmetric surface

Publié en ligne: 11 déc. 2014

Pages: 19 - 43

Reçu: 02 févr. 2014

DOI: https://doi.org/10.2478/aupcsm-2014-0003

© by Maria Robaszewska

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.