Pedro Morais
Departamento de Matemática, Universidade da Beira Interior

Abstract: Several authors have investigated whether on a given Riemannian manifold M^n there exists a totally geodesic foliation of codimension one, as well as the inverse problem of determining whether one can find a Riemannian metric on a manifold M^n with respect to which a given smooth foliation of codimension one on M^n becomes totally geodesic.
A related problem, but extrinsic in nature, may be formulated as follows: What are all Euclidean hypersurfaces f : M^n → R^{n+1}, n ≥ 3, that carry a foliation of codimension one with totally geodesic (complete or not) leaves?
This problem was solved by Dajczer , Rovenski and Tojeiro (2015).

In this talk we will study the spherical case.

This is a joint work with Susana Duarte Santos.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.