226,199 research outputs found
Geometry of quadrilateral nets: second Hamiltonian form
Discrete Darboux-Manakov-Zakharov systems possess two distinct Hamiltonian
forms. In the framework of discrete-differential geometry one Hamiltonian form
appears in a geometry of circular net. In this paper a geometry of second form
is identified.Comment: 6 page
BRST invariant formulation of spontaneously broken gauge theory in generalized differential geometry
Noncommutative geometry(NCG) on the discrete space successfully reproduces
the Higgs mechanism of the spontaneously broken gauge theory, in which the
Higgs boson field is regarded as a kind of gauge field on the discrete space.
We could construct the generalized differential geometry(GDG) on the discrete
space which is very close to NCG in case of .
GDG is a direct generalization of the differential geometry on the ordinary
manifold into the discrete one. In this paper, we attempt to construct the BRST
invariant formulation of spontaneously broken gauge theory based on GDG and
obtain the BRST invariant Lagrangian with the t'Hooft-Feynman gauge fixing
term.Comment: 15 page
Discrete Differential Geometry
This is the collection of extended abstracts for the 26 lectures and the open problem session at the fourth Oberwolfach workshop on Discrete Differential Geometry
Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey
This paper provides a tutorial and survey for a specific kind of illustrative
visualization technique: feature lines. We examine different feature line
methods. For this, we provide the differential geometry behind these concepts
and adapt this mathematical field to the discrete differential geometry. All
discrete differential geometry terms are explained for triangulated surface
meshes. These utilities serve as basis for the feature line methods. We provide
the reader with all knowledge to re-implement every feature line method.
Furthermore, we summarize the methods and suggest a guideline for which kind of
surface which feature line algorithm is best suited. Our work is motivated by,
but not restricted to, medical and biological surface models.Comment: 33 page
Curves of Finite Total Curvature
We consider the class of curves of finite total curvature, as introduced by
Milnor. This is a natural class for variational problems and geometric knot
theory, and since it includes both smooth and polygonal curves, its study shows
us connections between discrete and differential geometry. To explore these
ideas, we consider theorems of Fary/Milnor, Schur, Chakerian and Wienholtz.Comment: 25 pages, 4 figures; final version, to appear in "Discrete
Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 200
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