Conformal immersion of Riemannian products in low codimension

Abstract

We proved that a conformal immersion of $M_0^{n_0}\times M_1^{n_1}$ as an hipersurface in a Euclidean space must be an extrinsic product of immersions, under the assumption that $n_0,n_1\ge 2$ and that $M_0^{n_0}\times M_1^{n_1}$ is not conformally flat. We also stated a similar theorem for an arbitrary number of factors, more precisely, a conformal immersion $f:M_0^{n_0}\times \cdots \times M_k^{n_k}\to {\mathbb{R}}^{n+k}$ must be an extrinsic product of immersions if one of the factors admits a plane with vanishing curvature and the remaining factors are not flat.

9 pages