CONICET | Buscador de Institutos y Recursos Humanos

In this article we study spectral properties of flat Riemannianmanifolds, particularly, the determination of their $p$-formspectrum and the relations among different kinds ofisospectralities: $p$-isospectrality, Sunada isospectrality andlength isospectrality (i.e. with respect to lengths of closedgeodesics). We present the methods, main results and examplesobtained in several previous articles, and also some new materialon self-intersections of closed geodesics in this setting. We givenecessary and sufficient conditions for a closed geodesic toself-intersect, some applications to the existence of simple andnon-simple closed geodesics, and an example that shows that two`strongly´ isospectral manifolds can behave very differently inthis respect.