Duality between the generalized non-Hermitian Hatano-Nelson model in flat space and a Hermitian system in curved space

In this paper, we explore the possibility for the non-Hermiticity of the system originating from the curved space. We obtain a duality between a generalized non-Hermitian Hatano-Nelson model in d -dimensional flat space and a Hermitian system in 2 d -dimensional curved space, and give the metric of the curved space analytically. This duality shows the possibility of non-Hermiticity coming from the metric of the space, and provides a perspective on exploring non-Hermitian or Hermitian systems.