Opuscula Math. 38, no. 2 (2018), 201-252
https://doi.org/10.7494/OpMath.2018.38.2.201

Opuscula Mathematica

Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation

Mitsuo Kato
Toshiyuki Mano
Jiro Sekiguchi

Abstract. A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of Painlevé VI equation can be written by using polynomials or algebraic functions explicitly. The purpose of this paper is to construct potential vector fields corresponding to more than thirty non-equivalent algebraic solutions.

Keywords: flat structure, Painlevé VI equation, algebraic solution, potential vector field.

Mathematics Subject Classification: 34M56, 33E17, 35N10, 32S25.

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