Three-manifolds with many flat planes

Manifolds With Many Hyperbolic Planes

We construct examples of complete Riemannian manifolds having the property that every geodesic lies in a totally geodesic hyperbolic plane. Despite the abundance of totally geodesic hyperbolic planes, these examples are not locally homogenous.

Area-minimizing Projective Planes in Three-manifolds

Low dimensional flat manifolds with some classes of Finsler metric

Flat Riemannian manifolds are (up to isometry) quotient spaces of the Euclidean space R^n over a Bieberbach group and there are an exact classification of of them in 2 and 3 dimensions. In this paper, two classes of flat Finslerian manifolds are stuided and classified in dimensions 2 and 3.

Planes over Manifolds

Let us assume we are given an almost surely open, essentially Poisson system x. We wish to extend the results of [13] to dependent monoids. We show that O = −1. Unfortunately, we cannot assume that F ′′ is free. It is well known that Λ̂ is invariant and finite.

Seiberg-Witten Equations on Asymptotically Flat Three Manifolds

We construct the Seiberg-Witten theory on asymptotically flat three manifolds and describe the structure of the moduli space. The analysis should serve as the basis for many applications in 3-manifold topology, including a proof of the equivalence of the Seiberg-Witten invariant of 3-manifolds and the Reidemeister torsion [7].