Daniele Tiberio's seminar

[Antonio Lerario]

Seminar announcement

Speaker: Daniele Tiberio (SISSA)
Title: Geodesic distances on Banach manifolds.
Date and venue: Friday, July 30 at 5pm,
https://sissa-it.zoom.us/j/85675591787?pwd=TUo2VXpmcEhOU1paRzBXUWp2MU1odz09
Meeting ID: 856 7559 1787
Passcode: geometry

Abstract: In a connected Banach manifold, equipped with a weak Riemannian
metric, we show that the infimum of the lengths among all piecewise smooth
curves joining two points (namely, the geodesic "distance") does not define
a distance in general. We construct a simple counterxample in l^2. In
addition, if a weak Riemannian metric is left invariant on a Banach Lie
group, the geodesic "distance" still may not be a distance. Indeed, we
construct a counterexample in the infinite dimensional Heisenberg group,
and we show how the sectional curvatures can be calculated for some
specific planes, confirming a phenomenon first observed by Michor and
Mumford. This is a joint work in collaboration with Professor Valentino
Magnani (University of Pisa).

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*http://people.sissa.it/~lerario <http://people.sissa.it/~lerario>*