Zobrazeno 1 - 10
of 67
pro vyhledávání: '"PLATIS, Ioannis D."'
In this paper we describe the geodesics on the K\"ahler cone of the Heisenberg group. Furthermore we also prove that this is not a complete manifold.
Externí odkaz:
http://arxiv.org/abs/2407.10405
We consider the affine-additive group as a metric measure space with a canonical left-invariant measure and a left-invariant sub-Riemannian metric. We prove that this metric measure space is locally 4-Ahlfors regular and it is hyperbolic, meaning tha
Externí odkaz:
http://arxiv.org/abs/2407.04635
Let $\mathfrak{H}$ be the Heisenberg group. From the standard CR structure $\mathcal{H}$ of $\mathfrak{H}$ we construct the complex hyperbolic structure of the Siegel domain. Additionally, using the same minimal data for $\mathfrak{H}$, that is, its
Externí odkaz:
http://arxiv.org/abs/2304.08079
Publikováno v:
Bull. Korean Math. Soc. 2023; 60(1): 225-235
We show that metric bisectors with respect to the Kor\'anyi metric in the Heisenberg group are spinal spheres and vice versa. We also calculate explicitly their horizontal mean curvature.
Comment: 9 pages, 2 figures
Comment: 9 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2201.06073
Autor:
Platis, Ioannis D., Sun, Li-Jie
In this paper, we endow the right half plane with warped product metrics. The group of holomorphic isometries of all such metrics is isomorphic to the real additive group. Of our interest are two of those metrics: they have zero and unbounded negativ
Externí odkaz:
http://arxiv.org/abs/2111.07569
Autor:
Platis, Ioannis D.
A study of smooth contact quasiconformal mappings of the hyperbolic Heisenberg group is presented in this paper. Our main result is a Lifting Theorem; according to this, a symplectic quasiconformal mapping of the hyperbolic plane can be lifted to a c
Externí odkaz:
http://arxiv.org/abs/1909.11955
Autor:
Platis, Ioannis D., Sun, Li-Jie
Publikováno v:
Geom. Dedicata 214, 609-627 (2021)
We show that an open subset ${\mathfrak F}_4''$ of the ${\rm PU}(2,1)$ configuration space of four points in $S^3$ is in bijection with an open subset of %with a K\"ahler structure which is inherited from the one of ${\mathfrak H}^{\star}\times\mathb
Externí odkaz:
http://arxiv.org/abs/1906.06658
Autor:
Platis, Ioannis D.
We prove that the configuration space of equidistant triples on the Heisenberg group equipped with the Kor\'anyi metric, is isomorphic to a hypersurface of $\mathbb{R}^3$.
Comment: 10 pages, 1 figure
Comment: 10 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/1703.09420
Autor:
Platis, Ioannis D.
The torus $\mathbb{T}=S^1\times S^1$ appears as the ideal boundary $\partial_\infty AdS^3$ of the three-dimensional anti-de Sitter space $AdS^3$, as well as the F\"urstenberg boundary $\mathbb{F}(X)$ of the rank-2 symmetric space $X={\rm SO}_0(2,2)/{
Externí odkaz:
http://arxiv.org/abs/1703.05124
Autor:
Platis, Ioannis D., Sönmez, Nilgün
Publikováno v:
Turkish Journal of Mathematics (41) 1108-1120, 2017
We prove Ptolemaean Inequality and Ptolemaeus' Theorem in the closure complex hyperbolic plane endowed with the Cygan metric.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/1604.00473