122 research outputs found
Conformally Flat Circle Bundles over Surfaces
We classify conformally flat Riemannian manifolds which possesses a free
isometric action.Comment: 12 pages, Part of the author's PhD thesi
Harmonic maps in unfashionable geometries
We describe some general constructions on a real smooth projective 4-quadric
which provide analogues of the Willmore functional and conformal Gauss map in
both Lie sphere and projective differential geometry. Extrema of these
functionals are characterized by harmonicity of this Gauss map.Comment: plain TeX, uses bbmsl for blackboard bold, 20 page
A discrete version of the Darboux transform for isothermic surfaces
We study Christoffel and Darboux transforms of discrete isothermic nets in
4-dimensional Euclidean space: definitions and basic properties are derived.
Analogies with the smooth case are discussed and a definition for discrete
Ribaucour congruences is given. Surfaces of constant mean curvature are special
among all isothermic surfaces: they can be characterized by the fact that their
parallel constant mean curvature surfaces are Christoffel and Darboux
transforms at the same time. This characterization is used to define discrete
nets of constant mean curvature. Basic properties of discrete nets of constant
mean curvature are derived.Comment: 30 pages, LaTeX, a version with high quality figures is available at
http://www-sfb288.math.tu-berlin.de/preprints.htm
Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality
We show that the discrete principal nets in quadrics of constant curvature
that have constant mixed area mean curvature can be characterized by the
existence of a K\"onigs dual in a concentric quadric.Comment: 12 pages, 10 figures, pdfLaTeX (plain pdfTeX source included as bak
file
Lie geometry of flat fronts in hyperbolic space
We propose a Lie geometric point of view on flat fronts in hyperbolic space
as special omega-surfaces and discuss the Lie geometric deformation of flat
fronts
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