On some curvature energies for Legendrian knots in Heisenberg group.

Friday, June 28, 2019 - 9:00am - 10:00am
Keller 3-180
Marta Szumanska (University of Warsaw)
The Heisenberg group is a 3-dimensional Lie group homeomorphic to R^3. In each point of the group we consider 2-dimensional horizontal subspace (it agrees with a contact structure considered in contact geometry). A Legendrian knot is a knot which is represented by a curve which in each of its point is tangent to the horizontal plane in the point.

During the talk I will define knot energies for Legendrian knots in the Heisenberg group that are analogous to total curvature and to energies based on Menger curvature in Euclidean setting. I will describe their analytical and topological and geometrical (in the sense of geometry of Legendrian curves) properties.

The talk is based on a joint work with Katrin Faessler.