Structure quasi-conforme et dimension conforme d'après P. Pansu, M. Gromov et M. Bourdon
Subtleties concerning conformal tractor bundles
The realization of tractor bundles as associated bundles in conformal geometry is studied. It is shown that different natural choices of principal bundle with normal Cartan connection corresponding to a given conformal manifold can give rise to topologically distinct associated tractor bundles for the same inducing representation. Consequences for homogeneous models and conformal holonomy are described. A careful presentation is made of background material concerning standard tractor bundles and...
Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus.
Sur la conjecture de A. Lichnerowicz
Sur la première valeur propre des tores
Sur quelques propriétés conformes des surfaces de Borůvka de
Surfaces which contain many circles
We survey the results on surfaces which contain many circles. First, we give two analyses of shapes which always look round. Then we introduce the Blum conjecture: “A closed surface in E³ which contains seven circles through each point is a sphere”, and give some partial affirmative results toward the conjecture. Moreover, we study some surfaces which contain many circles through each point, for example, cyclides.
Tautness and Lie Sphere Geometry.
The action of conformal transformations on a Riemannian manifold.
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...
The Darboux mapping of canal hypersurfaces.
The Hurwitz Relation for Tori.
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The Non-Existence of Branch Points in Solutions to Certain Classes of Plateau Type Variational Problems.
Timelike Christoffel pairs in the split-quaternions
We characterize the Christoffel pairs of timelike isothermic surfaces in the four-dimensional split-quaternions. When restricting the receiving space to the three-dimensional imaginary split-quaternions, we establish an equivalent condition for a timelike surface in ℝ³₂ to be real or complex isothermic in terms of the existence of integrating factors.
Total bending of vector fields on Riemannian manifolds.
Traceless cubic forms on statistical manifolds and Tchebychev geometry
Geometry of traceless cubic forms is studied. It is shown that the traceless part of the cubic form on a statistical manifold determines a conformal-projective equivalence class of statistical manifolds. This conformal-projective equivalence on statistical manifolds is a natural generalization of conformal equivalence on Riemannian manifolds. As an application, Tchebychev type immersions in centroaffine immersions of codimension two are studied.
Transformation conforme de la courbure scalaire sur la sphère
Transitive conformal holonomy groups
For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act irreducibly...
Two models of non-Euclidean spaces generated by associative algebras