Related papers: On the existence of harmonic morphisms from three-…

We will investigate the local geometry of the surfaces in the $7$-dimensional Euclidean space associated to harmonic maps from a Riemann surface $\Sigma$ into $S^6$. By applying methods based on the use of harmonic sequences, we will…

As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions…

This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the…

Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they…

We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis of holomorphic forms on it. We present numerical examples,…

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus,…

We construct new complex-valued harmonic morphisms from Euclidean spaces from functions which are holomorphic with respect to Hermitian structures. In particular, we give the first global examples of complex-valued harmonic morphisms from…

In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism…

Invariant minimal surfaces in the real special linear group of degree 2 with canonical Riemannian and Lorentzian metrics are studied. Constant mean curvature surfaces with vertically harmonic Gau{\ss} map are classified.

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…

We classify rotational surfaces in a normed 3-space with rotationally symmetric norm whose principal curvatures satisfy a linear relation.

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

This paper is devoted to the study of the global properties of harmonically immersed Riemann surfaces in $\mathbb{R}^3.$ We focus on the geometry of complete harmonic immersions with quasiconformal Gauss map, and in particular, of those…

We show that any left invariant metric with harmonic curvature on a solvable Lie group is Ricci-parallel. We show the same result for any Lie group of dimension $\leq$ 6.

We consider complex manifolds that admit actions by holomorphic transformations of classical simple real Lie groups and classify all such manifolds in a natural situation. Under our assumptions, which require the group at hand to be…

We define a set of holomorphic functions in terms of the Hauptmodul of a quotient Riemann surface and prove that these functions are holomorphic on the upper half-plane. It is also shown that these functions are automorphic forms of weight…

We study the question of whether the topological quotient of a real linear representation of a simple three-dimensional compact Lie group is a manifold. We obtain an upper bound for the dimension of a representation whose quotient is a…