The geometry on a step 3 Grushin model
In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics...
| Main Authors: | , |
|---|---|
| Format: | Others |
| Language: | English |
| Published: |
Universität Potsdam
2004
|
| Subjects: | |
| Online Access: | http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26724 http://opus.kobv.de/ubp/volltexte/2008/2672/ |
| Summary: | In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis. |
|---|