Radial curvature and topology of Riemanni an manifolds

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19540107
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Fukuoka University
• Principal Investigator: SHIOHAMA Katsuhiro Fukuoka University, 理学部, 非常勤講師 (20016059)
• Project Period (FY): 2007 – 2009
• Keywords: リーマン計量 / 曲率 / 測地線

Research Abstract

完備点付きリーマン多様体の放射曲率が平面モデル又は球面モデルの放射曲率によって下から支えられている場合の多様体の位相を調べる事が本研究の目的である.基点を頂点の一つとする測地三角形の頂角に関するToponogovの比較定理が本研究に重要な役割を果たす.

Research Products

• [Journal Article] Complete real hypersurfaces in compact rank one symmetric spaces (2009)
  • Author(s): 濱田龍義, 塩濱勝博
  • Journal Title: Proc. Amer. Math. Soc. 137 Pages: 3905-3910
  • Peer Reviewed
• [Journal Article] The Steiner ratio conjecture of Gilbert-Pollak may still be open (2008)
  • Author(s): K. Kim, 印南信宏, 猿子幸弘, 塩濱勝博
  • Journal Title: Algorithmica
  • Peer Reviewed
• [Journal Article] An Integral formula for Lipschitz-Killing curvature and the critical points of height functions
  • Author(s): 塩濱勝博, Xu Hongwei
  • Journal Title: to appear in J. Geometric Analysis
  • Peer Reviewed
• [Presentation] Rdial curvature and topology of complete noncompact manifolds (2009)
  • Author(s): 塩濱勝博
  • Organizer: Global Analysis and Differential Geometry
  • Place of Presentation: Saga University
  • Year and Date: 2009-03-21
• [Presentation] Complete real hypersurfaces in hyperbolic spaces with constant holomorphic sectional curvature (2009)
  • Author(s): 塩濱勝博
  • Place of Presentation: 横浜市立大学数学セミナー
  • Year and Date: 2009-03-03
• [Presentation] 双曲空間内の完備実超曲面 (2009)
  • Author(s): 塩濱勝博
  • Organizer: リーマン幾何と幾何解析
  • Place of Presentation: 筑波大学研究集会
  • Year and Date: 2009-02-21
• [Presentation] 標準的射影空間内の完備実超曲面 (2008)
  • Author(s): 塩濱勝博
  • Organizer: Geometry and something
  • Place of Presentation: 福岡大学微分幾何研究会
  • Year and Date: 2008-11-21