Global Riemann-Finsler geometry

2012 Fiscal Year Final Research Report

• Project/Area Number: 22540097
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokai University
• Principal Investigator: SABAU Vasile Sorin 東海大学, 札幌教養教育センター, 准教授 (80364280)
• Project Period (FY): 2010 – 2012
• Keywords: 微分幾何学 / リーマン・フィンスラー構造

Research Abstract

This research clarifies global and topological properties of Riemann-Finsler structures. Precisely, we study the geodesics behavior, cut locus, topology of closed 3-manifolds carrying generalized Finsler structures.

Research Products

• [Journal Article] Two dimensional (α, β)-metrics with reversible geodesics (2013)
  • Author(s): M. I. Masca, S. V. Sabau, H. Shimada
  • Journal Title: Publicationes Mathematicae Debrecen Volume: 82/2 Pages: 485-501
  • Peer Reviewed
• [Journal Article] Finsler manifolds with reversible geodesics (2012)
  • Author(s): S. V. Sabau, H. Shimada
  • Volume: 57
  • Pages: 91-103
  • Peer Reviewed
• [Journal Article] Jacobi stability of dynamical systemsApplications in Gravitation and Cosmology (2012)
  • Author(s): C. Bohmer, T. Harko, S. V. Sabau
  • Journal Title: Advances in Theoretical and Mathematical Physics Volume: 16 Pages: 1-51
  • Peer Reviewed
• [Journal Article] The cut locus and distance function from a closed subset of a Finsler manifold (2012)
  • Author(s): M. Tanaka, S. V. Sabau
  • Pages: 投稿中
• [Journal Article] Kropina metrics and Zermelo navigation on Riemannian manifolds (2012)
  • Author(s): S. V. Sabau, R. Yoshikawa
  • Pages: 投稿中
• [Journal Article] Generalized Finsler structures on closed 3-manifolds (2012)
  • Author(s): S. V. Sabau, K. Shibuya, Gh. Pitis
  • Pages: 投稿中
• [Journal Article] Moving frames on generalized Finsler structures
  • Author(s): S. V. Sabau, K. Shibuya, H. Shimada
  • Journal Title: J. Korean Math. Soc Volume: Vol.49,No.6 Pages: 1229-1257
  • Peer Reviewed
• [Presentation] On the cut locus of Finsler manifolds (2012)
  • Author(s): S. V. Sabau
  • Organizer: 47-th Symposium on Finsler geometry
  • Place of Presentation: Kagoshima.
  • Year and Date: 20121100
• [Presentation] he structure of the cut locus of a Finsler surface (2012)
  • Author(s): S. V. Sabau
  • Organizer: The 3-rd KMITL-TKU Joint International Symposium on Mathematics and Applied mathematics
  • Place of Presentation: Pattaya, Thailand.
  • Year and Date: 20120700
• [Presentation] The cut locus structure for Riemann-Finsler surfaces (2011)
  • Author(s): S. V. Sabau
  • Organizer: The 46-th Symposium on Finsler geometry
  • Place of Presentation: Shizuoka
  • Year and Date: 20111100
• [Presentation] On the cut locus of Riemann-Finsler surfaces (2011)
  • Author(s): S. V. Sabau
  • Organizer: Geodesic theory methods in Finsler geometry
  • Place of Presentation: Kyoto
  • Year and Date: 20110900
• [Presentation] On the variational problem for Riemann-Finsler surfaces and related topics (2011)
  • Author(s): S. V. Sabau
  • Organizer: The 7-th International congress of Romanian mathematicians
  • Place of Presentation: Brasov, Romania.
  • Year and Date: 20110700
• [Presentation] Remarks on the geometry of magnetic geodesics (2010)
  • Author(s): S. V. Sabau
  • Organizer: The 45-th Symposium on Finsler geometry
  • Place of Presentation: Tokyo.
  • Year and Date: 20100900