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2014 | 13 |
Tytuł artykułu

On some flat connection associated with locally symmetric surface

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
13
Opis fizyczny
Daty
wydano
2014-12-01
otrzymano
2014-02-02
poprawiono
2014-05-04
online
2014-12-11
Twórcy
  • Institute of Mathematics Pedagogical University Podchorazych 2 30-084 Kraków Poland, robaszew@up.krakow.pl
Bibliografia
  • [1] J. Gancarzewicz, Zarys współczesnej geometrii rózniczkowej, Script, Warszawa 2010. Cited on 24.
  • [2] S. Kobayashi, K. Nomizu, Foundations of differential geometry, vol. I, Interscience Publishers, a division of John Wiley & Sons, New York-London 1963. Cited on 22.
  • [3] M. Marvan, On the spectral parameter problem, Acta Appl. Math. 109 (2010), no. 1, 239-255. Cited on 20.
  • [4] K. Nomizu, T. Sasaki, Affine differential geometry. Geometry of affine immersions. Cambridge Tracts in Mathematics 111, Cambridge University Press, Cambridge, 1994. Cited on 22.
  • [5] B. Opozda, Locally symmetric connections on surfaces, Results Math. 20 (1991), no. 3-4, 725-743. Cited on 21.
  • [6] B. Opozda, Some relations between Riemannian and affine geometry, Geom. Dedicata 47 (1993), no. 2, 225-236. Cited on 21 and 22.
  • [7] R. Sasaki, Soliton equations and pseudospherical surfaces, Nuclear Phys. B 154 (1979), no. 2, 343-357. Cited on 19 and 20.
  • [8] C.L. Terng, Geometric transformations and soliton equations, Handbook of geometric analysis, No. 2, 301-358, Adv. Lect. Math. (ALM), 13, Int. Press, Somerville, MA, 2010. Cited on 20.
  • [9] E. Wang, Tzitzéica transformation is a dressing action, J. Math. Phys. 47 (2006), no. 5, 053502, 13 pp. Cited on 20.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_aupcsm-2014-0003
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