TY  - JOUR
ID  - Kato2018
LB  - Kato2018
AU  - Kato, Mitsuo
AU  - Mano, Toshiyuki
AU  - Sekiguchi, Jiro
TI  - Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
ST  - Flat structure and potential vector fields related with algebraic solutions to Painlevé VI equation
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 2
SP  - 201
EP  - 252
DO  - https://doi.org/10.7494/OpMath.2018.38.2.201
UR  - https://doi.org/10.7494/OpMath.2018.38.2.201
AB  - 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.
KW  - flat structure
KW  - Painlevé VI equation
KW  - algebraic solution
KW  - potential vector field
SN  - 1232-9274
ER  -