Published online by Cambridge University Press: 22 January 2016
In the present paper, we are concerned with the problem to know whether two algebraic Riemann manifolds are isometric or not, where we mean Riemann manifolds of class CΩ (real algebraic smoothness or Nash category) simply by algebraic Riemann manifolds.
For this purpose we introduce notions of minimal differential polynomials and singular base points, both of which are isometry invariants. With the aid of these invariants, we give the following isometry theorem for algebraic Riemann manifolds: