4 citations · 10 across the 25 of their papers we have counts for
6 papers · 2 filters
Sub-Riemannian geodesics in the affine-additive group
Elia Bubani, Ioannis D. Platis, Georgios I. Simantiras +1
We derive the sub-Riemannian geodesics of the affine-additive group using the Pontryagin Maximum Principle (PMP) and compute the associated cut times. We then proceed to construct…
Bisectors in the Heisenberg group II
Gaoshun Gou, Joonhyung Kim, Ioannis D. Platis +1
Following previous work on metric bisectors with respect to the Korányi metric, we study here bisectors in the Heisenberg group equipped with the Carnot--Carathéodor…
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…