### On some flat connection associated with locally symmetric surface

#### Abstract

^{1}, ω

^{2}and from local connection form ω of ∇. The structural equations of (M, ∇) are equivalent to the condition dΩ-ΩΛΩ=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.

#### Keywords

#### Mathematics Subject Classification (2010)

#### References

Gancarzewicz, J. "Zarys współczesnej geometrii rózniczkowej." Warszawa: Script, 2010.

Kobayashi, S. and K. Nomizu. "Foundations of differential geometry. vol. I. New York-London: Interscience Publishers, a division of John Wiley & Sons, 1963.

Marvan, M. "On the spectral parameter problem." Acta Appl. Math. 109.1 (2010): 239-255.

Nomizu, K. and T. Sasaki. "Affine differential geometry. Geometry of affine immersions." Cambridge: Cambridge Tracts in Mathematics 111, Cambridge University Press, 1994.

Opozda, B. "Locally symmetric connections on surfaces." Results Math. 20.3-4 (1991): 725-743.

---. "Some relations between Riemannian and affine geometry." Geom. Dedicata 47.2 (1993): 225-236.

Sasaki, R. "Soliton equations and pseudospherical surfaces." Nuclear Phys. B 154.2 (1979): 343-357.

Terng, C.L. "Geometric transformations and soliton equations, Handbook of geometric analysis." No. 2. 301–358, Adv. Lect. Math. (ALM), 13, Somerville, MA: Int. Press, 2010.

Wang, E. "Tzitzéica transformation is a dressing action." J. Math. Phys. 47.5 (2006): 053502, 13 pp.

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