Geometry of geodesics for spaces with non-symmetric distances

• Project/Area Number: 15K13435
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Niigata University
• Principal Investigator: Innami Nobuhiro 新潟大学, 自然科学系, 教授 (20160145)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 測地線 / リーマン幾何学 / フィンスラー幾何学 / 非対称距離の幾何学 / カット―ローカス / 平行線の理論 / 測地円の漸近挙動 / ブーズマン関数 / 測地線の幾何学 / カットローカス / 測地円 / Finsler回転面 / トーラス

Outline of Final Research Achievements

A geodesic space is a metric space where geodesics are defined.Geometry of geodesics provides tools to study the topological and geometrical structure of geodesic spaces. Riemannian geometry, Finsler geometry and Alexandrov geometry are those examples.It is not studied systematically the space where distance is non-symmetric in that while it is always interested.I studied each property and theorem known in the symmetric case to get their generalizations and new results in the non-symmetric case by geometry of geodesics.I announced those result as some articles.

Research Products

• [Journal Article] Blaschke Finsler manifolds and actions of projective Randers changes on cut loci (2018)
  • Author(s): N. Innami, Y. Itokawa, T. Nagano, K. Shiohama
  • Journal Title: Trans. Amer. Maht. Soc. Volume: 印刷中
  • Peer Reviewed
• [Journal Article] The asymptotic behavior of geodesic circles in any 2-torus : A sub-mixing property (2018)
  • Author(s): Nobuhiro Innami, Toshiro Okura
  • Journal Title: Publ. Math. Debrecen Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Parallel axiom and the 2-nd order differentiability of Busemann functions, to appear in Publ. Math. Debrecen, (with Y. Itokawa (2018)
  • Author(s): N. Innami, Y. Itokawa, T. Nagano and K. Shiohama
  • Journal Title: Publ. Math. Debrecen Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Geodesics in a Finsler surface with one-parameter group of motions (2016)
  • Author(s): Nobuhiro Innami, Tetsuya Nagano, Katsuhiro Shiohama
  • Journal Title: Publ. Math. Debrecen Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Angular distribution of diameters for spheres and rays for planes (2015)
  • Author(s): Nobuhiro Innami, Yuya Uneme
  • Journal Title: Pacific J. Math. Volume: 277
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] トーラス上の測地線を参考にした曲面上の測地線 (2018)
  • Author(s): 印南信宏
  • Organizer: 研究会「直観幾何学2018」
• [Presentation] トーラス上の測地円の漸近挙動 (2018)
  • Author(s): 印南信宏
  • Organizer: 日本数学会年会
• [Presentation] カットローカスの最近点について (2017)
  • Author(s): 印南信宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 首都大学東京
  • Year and Date: 2017-03-25
• [Presentation] 非対称距離空間の幾何学 (2017)
  • Author(s): 印南信宏
  • Organizer: 研究会「直観幾何学2017」
  • Place of Presentation: 熊本大学
  • Year and Date: 2017-02-12
• [Presentation] カットローカスの最近点に関する Klingenberg 補題の Finsler 版 (2017)
  • Author(s): 印南信宏
  • Organizer: 研究会「測地線および関連する諸問題
  • Place of Presentation: 熊本大学
  • Year and Date: 2017-01-08
• [Presentation] 射影的ランダース変換とカットローカス (2017)
  • Author(s): 印南信宏
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Limit circles in a torus (2017)
  • Author(s): Nobuhiro Innami
  • Organizer: 52nd Symposium on Finsler Geometry
  • Int'l Joint Research
• [Presentation] 射影的ランダース変換とカットローカス (2017)
  • Author(s): 印南信宏
  • Organizer: 研究会「測地線及び関連する諸問題2018」
• [Presentation] The Finsler version of Klingenberg's lemma (2016)
  • Author(s): Nobuhiro Innami
  • Organizer: 51st Symposium on Finsler Geometry
  • Place of Presentation: 鹿児島県市町村自治会館
  • Year and Date: 2016-11-18
  • Int'l Joint Research
• [Presentation] 平行線の公理とBusemann関数の微分可能性 (2016)
  • Author(s): 印南信宏
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 関西大学
  • Year and Date: 2016-09-15
• [Presentation] Voronoi diagrams and cut loci in surfaces (2016)
  • Author(s): Nobuhiro Innami
  • Organizer: The Cut Locus : A bridge over differential geometry, optimal control, and transport
  • Place of Presentation: King Mongkut's Institute of Technology Ladkrabang, Thailand
  • Year and Date: 2016-08-03
  • Int'l Joint Research
• [Presentation] Finsler 回転面上の測地線の大域挙動 (2016)
  • Author(s): 印南 信宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 筑波大学
  • Year and Date: 2016-03-19
• [Presentation] Geodesics in a Finsler torus of revolution (2016)
  • Author(s): 印南 信宏
  • Organizer: 研究集会「測地線及び関連する諸問題」
  • Place of Presentation: 熊本大学教育学部
  • Year and Date: 2016-01-10
• [Presentation] Geodesics in a Finsler torus of revolution (2015)
  • Author(s): Nobuhiro Innami
  • Organizer: 19th International Workshop on: HERMITIAN-GRASSMANNIAN SUBMANIFOLDS AND ITS APPLICATIONS & the 10th KNUHGRG-OCAMI Joint Differential Geometry Workshop
  • Place of Presentation: Daejeon, Korea
  • Year and Date: 2015-10-27
  • Int'l Joint Research / Invited