Constructing Piecewise Flat Pseudo-Manifolds with Minimal Pseudo-Foliations

Details Constructing Piecewise Flat Pseudo-Manifolds with Minimal Pseudo-Foliations Constructing Piecewise Flat Pseudo-Manifolds with Minimal Pseudo-Foliations

2004-07-28

arxiv.org/abs/math/0407500v1

Mathematics

Differential Geometry

18 pages, 15 figures

Scientific paper

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of non-manifold point neighborhoods is done to preserve as much of the geometric, and vector space, structure of Euclidean space as possible. This enables structures, such as foliations and calibrations, to generalize over to pseudo-manifolds. The main result is that the cone of any compact topological surfaces can be given a piecewise flat metric structure that admits a pseudo-foliation by minimal surfaces. In some situations orientation reversing holonomy is an obstruction and in others it is just the opposite, a sufficient condition. Also foliations by minimal surfaces can extend across connect sum operations.

Affiliated with

Also associated with

No associations

Rating

Constructing Piecewise Flat Pseudo-Manifolds with Minimal Pseudo-Foliations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Constructing Piecewise Flat Pseudo-Manifolds with Minimal Pseudo-Foliations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing Piecewise Flat Pseudo-Manifolds with Minimal Pseudo-Foliations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-457472