Darboux transformations and isometric immersions of Riemannian products of space forms

Abstract

By using the Darboux transformation in Soliton theory, we give the explicit construction for local isometric immersions of the Riemannian product M₁^n₁(c₁)×M₂^n₂(c₂) into space forms M^m(c) with flat normal bundle via purely algebraic algorithm.