6 citations · 15 across the 10 of their papers we have counts for
10 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…
Equivariant basic cohomology of singular Riemannian foliations
Francisco C. Caramello
We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its i…
Leaf closures of Riemannian foliations: a survey on topological and geometric aspects of Killing foliations
Marcos M. Alexandrino, Francisco C. Caramello
A smooth foliation is Riemannian when its leaves are locally equidistant. The closures of the leaves of a Riemannian foliation on a simply connected manifold, or more generally of…
Introduction to orbifolds
Francisco C. Caramello
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, c…
Equivariant basic cohomology under deformations
Francisco C. Caramello, Dirk Toeben
There is a natural way to deform a Killing foliation with non-closed leaves, due to Ghys and Haefliger--Salem, into a closed foliation, i.e., a foliation whose leaves are all close…
Positively curved Killing foliations via deformations
Francisco C. Caramello, Dirk Toeben
We show that a compact manifold admitting a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex projective spaces, prov…