Differentialgeometrie der -dimensionalen Kugel- und Linienmannigfaltigkeiten im -dimensionalen euklidischen Raum
Discrete isothermic surfaces.
Equivariant connected sums of compact self-dual manifolds.
Equivariant tori which are critical points of the conformal total tension functional.
Se obtiene un nuevo método para obtener toros de Willmore en estructuras conformes de Kaluza-Klein sobre fibrados principales con fibra la circunferencia. Diversas aplicaciones de esta técnica son consideradas.
Erratum to: “Smooth metric measure spaces, quasi-Einstein metrics, and tractors”
The original version of the article was published in Central European Journal of Mathematics, 2012, 10(5), 1733–1762, DOI: 10.2478/s11533-012-0091-x. Unfortunately, it contains a typographical error in display of (27). Here we display the correct version of the equations.
Fibrés déterminants, déterminants régularisés et mesures sur les espaces de modules des courbes complexes
Foliations by surfaces of a peculiar class
We classify surfaces in 3-dimensional space forms which have all the local conformal invariants constant and show that compact 3-manifolds of nonzero constant sectional curvature admit no foliations by such surfaces.
Foliations making a constant angle with principal directions on ellipsoids
We study the global behavior of foliations of ellipsoids by curves making a constant angle with the lines of curvature.
Harmonic morphisms between riemannian manifolds
A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where vanishes. Every non-constant harmonic morphism is shown to be an open mapping....
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Histoire de la réductibilité du groupe conforme des variétés riemanniennes (1964-1994)
Homogeneous Cartan geometries
We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal automorphisms. The main result of this paper is that the above calculations are purely algorithmic. As an example of an homogeneous parabolic geometry we treat a conformal structure on the product of two spheres.
Hyperbolization of Euclidean ornaments.
Immersions minimales, première valeur propre du laplacien et volume conforme.
Invariant operations on manifolds with almost Hermitian symmetric structures. II: Normal Cartan connections.
Invariant operators on manifolds with almost Hermitian symmetric structures. I: Invariant differentiation.
Invariant prolongation of BGG-operators in conformal geometry
BGG-operators form sequences of invariant differential operators and the first of these is overdetermined. Interesting equations in conformal geometry described by these operators are those for Einstein scales, conformal Killing forms and conformal Killing tensors. We present a deformation procedure of the tractor connection which yields an invariant prolongation of the first operator. The explicit calculation is presented in the case of conformal Killing forms.
Kähler metrics associated to a real hypersurface.
Le volume conforme et ses applications d'après Li et Yau
Limit sets of Kleinian groups and conformally flat Riemannian manifolds.