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Propagation behavior of spreading geodesic circles in geodesically convex Finsler surfaces
http://hdl.handle.net/10191/00051770
http://hdl.handle.net/10191/00051770bc4b1510-c1e3-4078-8f79-632b87f38d92
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本文 (437.2 kB)
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要旨 (141.0 kB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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| 公開日 | 2020-08-31 | |||||
| タイトル | ||||||
| タイトル | Propagation behavior of spreading geodesic circles in geodesically convex Finsler surfaces | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_46ec | |||||
| 資源タイプ | thesis | |||||
| その他のタイトル | ||||||
| その他のタイトル | 測地的に凸なフィンスラー曲面上で広がる測地円の伝搬挙動 | |||||
| 著者 |
Kondo, Toshiki
× Kondo, Toshiki |
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| 著者別名 | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 177961 | |||||
| 姓名 | 近藤, 俊樹 | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | The geodesics are widely applied to studies of the geometrical structure and topological structure of manifolds. There exists a close link between the behavior of geodesics and curvature of manifolds. In general, a universal covering space has been used to study the behavior of geodesics in manifolds. In this way, the geodesic flows of compact Riemannian manifolds with negative curvature have been studied and contributed to the development of the dynamical systems. Moreover, H. Busemann and F. P. Pedersen have studied geodesics in a G-space whose universal covering spaces is straight, i.e., all geodesics are minimal. Their studies are applied to studies of geodesics in a 2-torus. N. Innami has studied the asymptotic behavior of geodesic circles in a 2-torus of revolution. N. Innami and T. Okura have proved for a Riemannian 2-torus T^2: ε-density of geodesic circles with sufficiently large radii. In this paper, we study the asymptotic behavior of geodesic circles in an orientable finitely connected and geodesically convex Finsler surface M with genus g ≥ 1. We have a generalization of their study if all geodesics in M are reversible, by using an intrinsic distance function and the Busemann function on its special covering space. In particular, this paper shows the global behavior of geodesics without assumptions on curvature and geodesically completeness of the surface. Furthermore, the absence of those assumptions is different from other previously studies of geodesics. Additionally, most of the proofs do not need the reversibility assumption on geodesics. | |||||
| 書誌情報 | p. 1-42 | |||||
| 著者版フラグ | ||||||
| 値 | ETD | |||||
| 学位名 | ||||||
| 学位名 | 博士(理学) | |||||
| 学位授与機関 | ||||||
| 学位授与機関名 | 新潟大学 | |||||
| 学位授与年月日 | ||||||
| 学位授与年月日 | 2020-03-23 | |||||
| 学位授与番号 | ||||||
| 学位授与番号 | 13101甲第4759号 | |||||
| 学位記番号 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | 新大院博(理)甲第449号 | |||||
