# On some flat connection associated with locally symmetric surface

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2014)

- Volume: 13, Issue: 1, page 19-43
- ISSN: 2300-133X

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topMaria Robaszewska. "On some flat connection associated with locally symmetric surface." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 13.1 (2014): 19-43. <http://eudml.org/doc/268837>.

@article{MariaRobaszewska2014,

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.},

author = {Maria Robaszewska},

journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},

keywords = {principal fibre bundle; Gauss curvature; local connection form},

language = {eng},

number = {1},

pages = {19-43},

title = {On some flat connection associated with locally symmetric surface},

url = {http://eudml.org/doc/268837},

volume = {13},

year = {2014},

}

TY - JOUR

AU - Maria Robaszewska

TI - On some flat connection associated with locally symmetric surface

JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

PY - 2014

VL - 13

IS - 1

SP - 19

EP - 43

AB - 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.

LA - eng

KW - principal fibre bundle; Gauss curvature; local connection form

UR - http://eudml.org/doc/268837

ER -

## References

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