Geodesic
Klein's Fundamental $2$-Form of Second Kind for the $C_{ab}$ Curves
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we derive the exact formula of Klein's fundamental $2$-form of second kind for the so-called $C_{ab}$ curves. The problem was initially solved by Klein in the 19th century for the hyper-elliptic curves, but little progress had been seen for its extension for more than 100 years. Recently, it has been addressed by several authors, and was solved for subclasses of the $C_{ab}$ curves whereas they found a way to find its individual solution numerically. The formula gives a standard cohomological basis for the curves, and has many applications in algebraic geometry, physics, and applied mathematics, not just analyzing sigma functions in a general way.
Keywords: $C_{ab}$ curves; Klein's fundamental $2$-form of second kind; cohomological basis; symmetry. 
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Joe Suzuki. Klein's Fundamental $2$-Form of Second Kind for the $C_{ab}$ Curves. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a16/

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