Existence of closed geodesics through a regular point on translation surfaces
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Annalen"
DOI: 10.1007/s00208-019-01897-2
Abstract: We show that on any translation surface, if a regular point is contained in some simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in $${\mathbb {RP}}^1$$… read more here.
Keywords: closed geodesics; simple closed; translation; translation surfaces ... See more keywords
Classifications of Translation Surfaces in Isotropic Geometry with Constant Curvature
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DOI: 10.1007/s11253-020-01785-y
Abstract: UDC 515.12 We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvatures under the condition that at least one of translating curves lies in a plane. read more here.
Keywords: geometry; surfaces isotropic; isotropic geometry; classifications translation ... See more keywords
Crossing the Transcendental Divide: From Translation Surfaces to Algebraic Curves
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DOI: 10.1080/10586458.2023.2203413
Abstract: We study constructing an algebraic curve from a Riemann surface given via a translation surface, which is a collection of finitely many polygons in the plane with sides identified by translation. We use the theory… read more here.
Keywords: algebraic curves; transcendental divide; crossing transcendental; translation surfaces ... See more keywords
Weighted minimal translation surfaces in the Galilean space with density
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DOI: 10.1515/math-2017-0043
Abstract: Abstract Translation surfaces in the Galilean 3-space G3 have two types according to the isotropic and non-isotropic plane curves. In this paper, we study a translation surface in G3 with a log-linear density and classify… read more here.
Keywords: density; galilean space; surfaces galilean; translation ... See more keywords
Minimal translation surfaces in the three-dimensional Heisenberg group
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DOI: 10.2298/fil1906583r
Abstract: We define and classify minimal translation surfaces in the 3-dimensional Heisenberg group H(1,1). read more here.
Keywords: heisenberg group; dimensional heisenberg; minimal translation; translation surfaces ... See more keywords