5 papers · 1 filter
Tanaka-Webster curvatures of surfaces in 3D Lie groups with a CR structure
Ioannis D. Platis, Dimitrios Tsolis
We consider the Tanaka-Webster geometry of surfaces embedded in a 3-dimensional Lie group with a CR structure inherited by a contact form. We define the notions of Gauss and mean c…
An isoperimetric inequality on three-dimensional, contact, non-unimodular Lie groups
Ioannis D. Platis, Georgios I. Simantiras
We prove an isoperimetric inequality for compact bodies bounded by surfaces embedded into a connected, contact, non-unimodular 3-dimensional Lie group.
Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups
Elia Bubani, Andrea Pinamonti, Ioannis D. Platis +1
In this paper we study horizontal curvatures for surfaces embedded in three-dimensional contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we derive explic…
On the sub-Riemannian geometry of the quaternionic Heisenberg group
Joonhyung Kim, Ioannis D. Platis, Li-Jie Sun
Utilizing the framework of quaternionic contact geometry, we define a sequence of Riemannian metrics on the quaternionic Heisenberg group by r…
Stretch maps on the affine-additive group
Z. M. Balogh, E. Bubani, I. D. Platis
We define linear and radial stretch maps in the affine-additive group, and prove that they are minimizers of the mean quasiconformal distortion functional. For the proofs we use a…