On superintegrable systems with a position-dependent mass in polar-like coordinates**Project supported in part by the National Natural Science Foundation of China (Grant No. 11701009), the Natural Science Research Project of Universities in Anhui, China (Grant No. KJ2017A363), and the Natural Science Fund of Anhui Province, China (Grant Nos. 1908085MA01 and 1908085MA22).

Abstract

For a superintegrable system defined in plane polar-like coordinates introduced by Szumiński et al. and studied by Fordy, we show that the system with a position-dependent mass is separable in three distinct coordinate systems. The corresponding separation equations and additional integrals of motion are derived explicitly. The closure algebra of integrals is deduced. We also make a generalization of this system by employing the classical Jacobi method. Lastly a sufficient condition which ensures flatness of the underlying space is derived via explicit calculation.