Loxodromes on Invariant Surfaces in Three-Manifolds

Autor(es)

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

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Mediterranean Journal of Mathematics; v. 17, n. 1 FEB 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/24707-4 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático