Schouten tensor equations in conformal geometry with prescribed boundary metric.
Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics
We study the Jones and Tod correspondence between selfdual conformal -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl -manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kähler metrics and hypercomplex structures with symmetry. We also show that in the presence...
Smooth metric measure spaces, quasi-Einstein metrics, and tractors
We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.
Some Global Theorems on Non-Complete Surfaces
Some representations of affine conformal transformations of Minkowski space.
Some theorems on compact conformally symmetric Riemannian spaces
Spezielle äquiforme Zwangläufe
In der Ebene kann ein äquiformer Zwanglauf so bestimmt werden, daß jede Gerade einer beweglichen Ebene in einer festen Ebene eine zykloidale Kurve mit demselben Modul umhüllt. Das Problem wird ebenfalls im Raum gelöst und verallgemeinert.
Structure of the kernel of higher spin Dirac operators
Polynomials on with values in an irreducible -module form a natural representation space for the group . These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on with values in these modules.
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.