Loxodromes on Invariant Surfaces in Three-Manifolds

Author(s)

Caddeo, Renzo ^[1] ; Onnis, Irene I. ^[2] ; Piu, Paola ^[1]

Affiliation

^[1] Univ Cagliari, Dipartimento Matemat & Informat, Via Osped 72, I-09124 Cagliari - Italy

^[2] Univ Sao Paulo, ICMC, Dept Matemat, CP 668, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Mediterranean Journal of Mathematics; v. 17, n. 1 FEB 2020.
• Web of Science Citations: 0

Abstract

In this paper, we prove some results concerning the loxodromes on an invariant surface in a three-dimensional Riemannian manifold, a part of which generalizes classical results about loxodromes on rotational surfaces in R-3. In particular, we show how to parametrize a loxodrome on an invariant surface of H-2 x R and H-3, and we exhibit the loxodromes of some remarkable minimal invariant surfaces of these spaces. In addition, we give an explicit description of the loxodromes on an invariant surface with constant Gauss curvature. (AU)

• FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants