Nikos Georgiou

activity

20072026

most citedA characterization of Weingarten surfaces in hyperbolic 3-space

15 citations · 57 across the 19 of their papers we have counts for

collaborators

19 papers

math.DG2026

Isotropic submanifolds of $T S^{n}$ and their focal sets

Nikos Georgiou, Brendan Guilfoyle, Morgan Robson

Families of oriented lines in $R^{n + 1}$ are studied via their identification with submanifolds of $T S^{n}$ . In particular, families of oriented lines which are orth…

math.DG2024

Minimal surfaces in the Riemannian product of surfaces

Nikos Georgiou, Brendan Guilfoyle

Minimal surfaces in the Riemannian product of surfaces of constant curvature have been considered recently, particularly as these products arise as spaces of oriented geodesics of…

math.DG2022

Null hypersurfaces in 4-manifolds endowed with a product structure

Nikos Georgiou

In a 4-manifold, the composition of a Riemannian Einstein metric with an almost paracomplex structure that is isometric and parallel, defines a neutral metric that is conformally f…

math.DG2021★ 4 cited

Almost Paracomplex Structures on 4-Manifolds

Nikos Georgiou, Brendan Guilfoyle

Reflection in a line in Euclidean 3-space defines an almost paracomplex structure on the space of all oriented lines, isometric with respect to the canonical neutral Kaehler metric…

math.DG2019

A para-Kaehler structure in the space of oriented geodesics in a real space form

Nikos Georgiou

In this article, we construct a new para-Kähler structure $(G, J, Ω)$ in the space of oriented geodesics $L (M)$ in a non-flat, real space form $M$ . We…

math.DG2018★ 5 cited

A new geometric structure on tangent bundles

Nikos Georgiou, Brendan Guilfoyle

For a Riemannian manifold $(N, g)$ , we construct a scalar flat metric $G$ in the tangent bundle $T N$ . It is locally conformally flat if and only if either, $N$ is a 2-dimensional ma…

math.DG2016★ 1 cited

Hopf hypersurfaces in spaces of oriented geodesics

Nikos Georgiou, Brendan Guilfoyle

A Hopf hypersurface in a (para-)Kaehler manifold is a real hypersurface for which one of the principal directions of the second fundamental form is the (para-)complex dual of the n…

math.DG2016★ 2 cited

The causal topology of neutral 4-manifolds with null boundary

Nikos Georgiou, Brendan Guilfoyle

This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we…

math.DG2016

Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric

Martha P. Dussan, Nikos Georgiou, Martin Magid

We investigate minimal surfaces in products of two-spheres $S_{p}^{2} \times S_{p}^{2}$ , with the neutral metric given by $(g, - g)$ . Here ${\mathbb S}^2_p\subset {\mathbb…

math.DG2014★ 1 cited

On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms

Nikos Georgiou, Guillermo Antonio Lobos Villagra

We prove that a deformation of a hypersurface in a $(n + 1)$ -dimensional real space form $S_{p, 1}^{n + 1}$ induce a Hamiltonian variation of the normal congruence in the spac…

math.DG2014★ 4 cited

Lagrangian immersions in the product of Lorentzian two manifold

Nikos Georgiou

For Lorentzian 2-manifolds $(Σ_{1}, g_{1})$ and $(Σ_{2}, g_{2})$ we consider the two product para-Kähler structures $(G^{ε}, J, Ω^{ε})$ defined on the product four manifold $Σ_{1} \times Σ_{2}$ , with $ε…

math.DG2013★ 4 cited

Marginally trapped surfaces in spaces of oriented geodesics

Brendan Guilfoyle, Nikos Georgiou

We investigate the geometric properties of marginally trapped surfaces (surfaces which have null mean curvature vector) in the spaces of oriented geodesics of Euclidean 3-space and…

math.DG2013★ 8 cited

On minimal Lagrangian surfaces in the product of Riemannian two manifolds

Nikos Georgiou

Let $(Σ_{1}, g_{1})$ and $(Σ_{2}, g_{2})$ be connected, complete and orientable Riemannian two manifolds. Consider the two canonical Kähler structures $(G^{ε}, J, Ω^{ε})$ on the product 4-manifold…

math.DG2012

Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds

Henri Anciaux, Nikos Georgiou

Let L be a Lagrangian submanifold of a pseudo- or para-Kähler manifold which is H-minimal, i.e. a critical point of the volume functional restricted to Hamiltonian variations. We d…

math.DG2010★ 2 cited

On maximal surfaces in the space of oriented geodesics of hyperbolic 3-space

Nikos Georgiou

We study area-stationary, or maximal, surfaces in the space $L (H^{3})$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler stru…

math.DG2009★ 9 cited

The Blaschke-Lebesgue problem for constant width bodies of revolution

Henri Anciaux, Nikos Georgiou

We prove that among all constant width bodies of revolution, the minimum of the ratio of the volume to the cubed width is attained by the constant width body obtained by rotation o…

math.DG2008★ 2 cited

Totally Null Surfaces in Neutral Kaehler 4-Manifolds

Nikos Georgiou, Brendan Guilfoyle, Wilhelm Klingenberg

We study the totally null surfaces of the neutral Kaehler metric on certain 4-manifolds. The tangent spaces of totally null surfaces are either self-dual ( $α$ -planes) or anti-self-…

math.DG2007★ 15 cited

A characterization of Weingarten surfaces in hyperbolic 3-space

Nikos Georgiou, Brendan Guilfoyle

We study 2-dimensional submanifolds of the space $L (H^{3})$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. Su…

math.DG2007

On the space of oriented geodesics of hyperbolic 3-space

Nikos Georgiou, Brendan Guilfoyle

We construct a Kähler structure ( $J, Ω, G$ ) on the space $L (H^{3})$ of oriented geodesics of hyperbolic 3-space $H^{3}$ and investi…

Isotropic submanifolds of TSn and their focal sets

Minimal surfaces in the Riemannian product of surfaces

Null hypersurfaces in 4-manifolds endowed with a product structure

Almost Paracomplex Structures on 4-Manifolds

A para-Kaehler structure in the space of oriented geodesics in a real space form

A new geometric structure on tangent bundles

Hopf hypersurfaces in spaces of oriented geodesics

The causal topology of neutral 4-manifolds with null boundary

Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric

On Hamiltonian minimal submanifolds in the space of oriented geodesics in real space forms

Lagrangian immersions in the product of Lorentzian two manifold

Marginally trapped surfaces in spaces of oriented geodesics

On minimal Lagrangian surfaces in the product of Riemannian two manifolds

Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kähler manifolds

On maximal surfaces in the space of oriented geodesics of hyperbolic 3-space

The Blaschke-Lebesgue problem for constant width bodies of revolution

Totally Null Surfaces in Neutral Kaehler 4-Manifolds

A characterization of Weingarten surfaces in hyperbolic 3-space

On the space of oriented geodesics of hyperbolic 3-space

Isotropic submanifolds of $T S^{n}$ and their focal sets