Topics in Lorentzian and Finsler Geometry: geodesic flow and isometry group
Orthogonal geodesics in manifolds with singular boundary. Applications to the theo...
| Full text | |
| Author(s): |
Cosac, Gregory
;
Doria, Cayo
Total Authors: 2
|
| Document type: | Journal article |
| Source: | MATHEMATICAL RESEARCH LETTERS; v. 29, n. 4, p. 41-pg., 2022-01-01. |
| Abstract | |
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove that their systoles are dense in the positive real numbers. Furthermore, this leads to a construction, for each genus g >= 2, of infinite families of semiarithmetic surfaces with pairwise distinct invariant trace fields, giving a negative answer to a conjecture of B. Jeon. Finally, for any semi-arithmetic surface we find a sequence of congruence coverings with logarithmic systolic growth and, for the special case of surfaces admitting modular embedding, we are able to exhibit explicit constants. (AU) | |
| FAPESP's process: | 18/15750-9 - Closed curves on hyperbolic manifolds. |
| Grantee: | Cayo Rodrigo Felizardo Dória |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |