• 研究課題をさがす
  • 研究者をさがす
  • KAKENの使い方
  1. 課題ページに戻る

2014 年度 実施状況報告書

Geometry of geodesics of Riemannian and Finsler manifolds

研究課題

研究課題/領域番号 25400075
研究機関東海大学

研究代表者

SABAU Vasile.Sor  東海大学, 札幌教養教育センター, 教授 (80364280)

研究期間 (年度) 2013-04-01 – 2016-03-31
キーワードFinsler manifolds / Riemannian manifolds / Busemann functions / cut locus / convex functions / flag curvature / level sets / distance function
研究実績の概要

In this year I have extensively studied the Busemann functions on forward completely, non-compact Finsler manifold. In special I have clarified the relation between the set of co-points and the cut locus of the level set of a Busemann function. This research provides new results not only for Finsler manifolds, but also for Riemannian manifolds as well.

In the quest of concrete examples of Busemann functions I have considered Finsler surfaces of revolution. I have studied the differential geometry of these surfaces in order to clarify the geodesics behavior, cut locus, poles, rays and behavior of Busemann functions.

現在までの達成度 (区分)
現在までの達成度 (区分)

3: やや遅れている

理由

The research is progressing slightly delayed than initially planned because the research of Busemann functions on complete, non-compact Finsler manifolds took much more time than I thought. Indeed, the facts that the geodesics are not reversible and that the flag curvature, the Finslerian equivalent of the sectional curvature, lives on TM and not on the base manifold M bring challenging difficulties. Finally, almost all difficulties were surmounted, but this took little more time that expected.

今後の研究の推進方策

I intend to catch up the delay occurred from the reasons explained above and to realize the initial proposed research plan. The topics remained are the conditions for a Finsler manifold to have cut locus with integer Hausdorff dimension, convexity of the Busemann function and implications of the existence of convex functions with compact levels on the isometry groups properties of a Finsler manifold. I intend to study thoroughly these topics in 2015.

次年度使用額が生じた理由

購入予定の専門書は受注できなくて科研費使用可能な期間に間に合わなかったため

次年度使用額の使用計画

書籍を購入すること

  • 研究成果

    (6件)

すべて 2014

すべて 雑誌論文 (3件) (うち査読あり 3件、 謝辞記載あり 2件) 学会発表 (3件) (うち招待講演 1件)

  • [雑誌論文] Metric structures associated to Finsler metrics2014

    • 著者名/発表者名
      Sorin V. Sabau, Kazuhiro Shibuya, Hideo Shimada
    • 雑誌名

      Publ. Math. Debrecen

      巻: vol. 84, no. 1-2 ページ: 89-103

    • 査読あり
  • [雑誌論文] Generalized Finsler structures on closed 3-manifolds2014

    • 著者名/発表者名
      Sorin V. Sabau, Kazuhiro Shibuya, Gheorghe Pitis
    • 雑誌名

      Tohoku Math. Journal

      巻: vol. 66, no. 3 ページ: 321-353

    • 査読あり / 謝辞記載あり
  • [雑誌論文] Some remarks on the Geometry of Kropina spaces2014

    • 著者名/発表者名
      Ryozo Yoshikawa, Sorin V. Sabau
    • 雑誌名

      Publ. Math. Debrecen

      巻: vol. 84, no. 3-4 ページ: 483-496

    • 査読あり / 謝辞記載あり
  • [学会発表] Some remarks on the geometry of a Randers rotational surface of revolution2014

    • 著者名/発表者名
      Sorin V. Sabau
    • 学会等名
      The 49-th Finsler Geometry Symposium
    • 発表場所
      Nagasaki
    • 年月日
      2014-12-04 – 2014-12-07
  • [学会発表] Variational Problems and EDS2014

    • 著者名/発表者名
      Sorin V. Sabau
    • 学会等名
      Hiroshima University annual conference
    • 発表場所
      Hiroshima University, Hiroshima
    • 年月日
      2014-10-08 – 2014-10-10
  • [学会発表] Remarks on the Geometry of Geodesics on Finsler manifolds2014

    • 著者名/発表者名
      Sorin V. Sabau
    • 学会等名
      Ramanujan Mathematical Society
    • 発表場所
      Pune University, India
    • 年月日
      2014-06-23 – 2014-06-27
    • 招待講演

URL: 

公開日: 2016-05-27  

サービス概要 検索マニュアル よくある質問 お知らせ 利用規程 科研費による研究の帰属

Powered by NII kakenhi