3 papers
math.DG2024
The Michor-Mumford conjecture in Hilbertian H-type groups
Valentino Magnani, Daniele Tiberio
We introduce infinite dimensional Hilbertian H-type groups equipped with weak, graded, left invariant Riemannian metrics. For these Lie groups, we show that the vanishing of the ge…
math.DG2021
On the Michor-Mumford phenomenon in the infinite dimensional Heisenberg group
Valentino Magnani, Daniele Tiberio
In the infinite dimensional Heisenberg group, we construct a left invariant weak Riemannian metric that gives a degenerate geodesic distance. The same construction yields a degener…
math.DG2019
A remark on vanishing geodesic distances in infinite dimensions
Valentino Magnani, Daniele Tiberio
We observe that a vanishing geodesic distance arising from a weak Riemannian metric in a Hilbert manifold can be constructed.