The conjugate locus on convex surfaces
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915233990180864 |
|---|---|
| author | Waters, Thomas |
| author_facet | Waters, Thomas |
| contents | The conjugate locus of a point on a surface is the envelope of geodesics emanating radially from that point. In this paper we show that the conjugate loci of generic points on convex surfaces satisfy a simple relationship between the rotation index and the number of cusps. As a consequence we prove the `vierspitzensatz': the conjugate locus of a generic point on a convex surface must have at least four cusps. Along the way we prove certain results about evolutes in the plane and geodesic curvature. (Note: this is a corrected version of the original paper, see comment on page 5 and Appendix B). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_00278 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The conjugate locus on convex surfaces Waters, Thomas Differential Geometry The conjugate locus of a point on a surface is the envelope of geodesics emanating radially from that point. In this paper we show that the conjugate loci of generic points on convex surfaces satisfy a simple relationship between the rotation index and the number of cusps. As a consequence we prove the `vierspitzensatz': the conjugate locus of a generic point on a convex surface must have at least four cusps. Along the way we prove certain results about evolutes in the plane and geodesic curvature. (Note: this is a corrected version of the original paper, see comment on page 5 and Appendix B). |
| title | The conjugate locus on convex surfaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1806.00278 |