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Construction of BGG sequences for AHS structures

Lukáš Krump (2001)

Commentationes Mathematicae Universitatis Carolinae

This paper gives a description of a method of direct construction of the BGG sequences of invariant operators on manifolds with AHS structures on the base of representation theoretical data of the Lie algebra defining the AHS structure. Several examples of the method are shown.

Construction of compact constant mean curvature hypersurfaces with topology

Mohamed Jleli (2012)

Annales de l’institut Fourier

In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.

Contact elements on fibered manifolds

Ivan Kolář, Włodzimierz M. Mikulski (2003)

Czechoslovak Mathematical Journal

For every product preserving bundle functor T μ on fibered manifolds, we describe the underlying functor of any order ( r , s , q ) , s r q . We define the bundle K k , l r , s , q Y of ( k , l ) -dimensional contact elements of the order ( r , s , q ) on a fibered manifold Y and we characterize its elements geometrically. Then we study the bundle of general contact elements of type μ . We also determine all natural transformations of K k , l r , s , q Y into itself and of T ( K k , l r , s , q Y ) into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms...

Courbure discrète ponctuelle

Vincent Borrelli (2006/2007)

Séminaire de théorie spectrale et géométrie

Soient S une surface de l’espace euclidien 𝔼 3 et M un ensemble de triangles euclidiens formant une approximation linéaire par morceaux de S autour d’un point P S , la courbure discrète ponctuelle K d ( P ) au sommet P de M est, par définition, le quotient du défaut angulaire par la somme des aires des triangles ayant P comme sommet. Un problème naturel est d’estimer la différence entre cette courbure discrète K d ( S ) et la courbure lisse K ( P ) de S en P . Nous présentons dans cet article des résultats obtenus dans [4], [5],...

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