On some flat connection associated with locally symmetric surface
For every two-dimensional manifold M with locally symmetric linear connection nabla, endowed also with nabla-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 f...
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| Format: | Article |
| Language: | deu |
| Published: |
Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
2014-04-01
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| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/154 |
| Summary: | For every two-dimensional manifold M with locally symmetric linear connection nabla, endowed also with
nabla-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 connection is a
R(G)-valued 1-form Omega build from the dual basis omega1, omega 2 and from local connection form omega of nabla. The structural equations of (M, nabla) are equivalent to the
condition dOmega-Omega Lambda Omega=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 surface. |
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| ISSN: | 2081-545X 2300-133X |