5 papers
Polar and torus manifolds
Francisco C. Caramello, Dirk Toeben
We show that quasitoric manifolds can be equipped with an invariant metric for which the torus action is polar. More generally, we show that an infinitesimally polar action of a to…
Blown-up singular Riemannian foliations
Francisco C. Caramello, Laura Ribeiro dos Santos
We investigate new properties and applications of the blow-up desingularization method in the context of singular Riemannian foliations. First, we relate the dynamics of such a fol…
Transverse sphere theorems for Riemannian foliations
Francisco C. Caramello, Francisco A. Neubauer
We extend the classical theory of sphere theorems to the transverse geometry of Riemannian foliations. In this setting, we establish transverse analogues of the Grove-Shiohama diam…
A Hadamard theorem in transversely affine geometry with applications to affine orbifolds
Francisco C. Caramello, Henrique A. Puel Martins, Ivan P. Costa e Silva
We introduce and investigate a novel notion of transversely affine foliation, comparing and contrasting it to the previous ones in the literature. We then use it to give an extensi…
Transverse Geometry of Lorentzian foliations with applications to Lorentzian orbifolds
Francisco C. Caramello, Henrique A. Puel Martins, Ivan P. Costa e Silva
We prove a transverse diameter theorem in the context of Lorentzian foliations, which can be interpreted as a Hawking--Penrose-type singularity theorem for timelike geodesics trans…