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 R3. In particular, we show how to parametrize a loxodrome on an invariant surface of H2× R and H3, 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.
Loxodromes on Invariant Surfaces in Three-Manifolds
Caddeo R.Membro del Collaboration Group
;Onnis I. I.;Piu P.
Membro del Collaboration Group
2020-01-01
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 R3. In particular, we show how to parametrize a loxodrome on an invariant surface of H2× R and H3, 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.
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