Resumen de Global Models of Riemannian Metrics.

Fernando Varela García , J. Fontanillas

• In this paper we give certain Riemannian metrics on the manifolds Sn-1 x S1 and Sn (n = 2), which have the property to determine these manifolds, up to diffeomorphisms.

  The global expressions used for Riemannian metrics are based on the global expression for exterior forms studied in [4]. In [3] one finds certain metrics using global expressions that differ from the type we propose.

  To some extent, Theorem 3 is a generalization for metrics in an arbitrary dimension, of a theorem proved in [2] for certain volume forms on surfaces.