Behavior of distant maximal geodesics in finitely connected complete two-dimensional Riemannian manifolds II

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We study the behavior of maximal geodesics in a finitely connected complete two-dimensional Riemannian manifold M admitting curvature at infinity. In the case where M is homeomorphic to ℝ2 the Cohn-Vossen theorem states that the total curvature of M, say c(M), is ≤2π. We already studied the case c(M) < 2π in our previous paper. So we study the behavior of geodesics in M with total curvature 2π in this paper. Next we consider the case where M has nonempty boundary. In order to know the behavior of distant geodesics in M with boundary, it is useful to investigate the 'visual image' of the boundary of M. The latter half of this paper will be spent to study the asymptotic behavior of the visual image of a subset of M with located point tending to infinity.

本文言語English
ページ(範囲)1-32
ページ数32
ジャーナルGeometriae Dedicata
103
1
DOI
出版ステータスPublished - 2004 2月

ASJC Scopus subject areas

  • 幾何学とトポロジー

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