A TOPOLOGICAL SPLITTING THEOREM FOR WEIGHTED ALEXANDROV SPACES

• KUWAE KAZUHIRO

  Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University

• SHIOYA TAKASHI

  Mathematical Institute, Tohoku University

抄録

Under an infinitesimal version of the Bishop-Gromov relative volume comparison condition for a measure on an Alexandrov space, we prove a topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove an isometric splitting theorem for Riemannian manifolds with singularities of nonnegative (Bakry-Emery) Ricci curvature.

収録刊行物

• Ｔｏｈｏｋｕ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｊｏｕｒｎａｌ，　Ｓｅｃｏｎｄ　Ｓｅｒｉｅｓ

  Ｔｏｈｏｋｕ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｊｏｕｒｎａｌ，　Ｓｅｃｏｎｄ　Ｓｅｒｉｅｓ 63 (1), 59-76, 2011

  東北大学大学院理学研究科数学専攻

キーワード

• splitting theorem
• Ricci curvature
• Bishop-Gromov inequality

詳細情報

• CRID: 1390282680094479744
• NII論文ID: 110008425969
• NII書誌ID: AA00863953
• DOI: 10.2748/tmj/1303219936
• ISSN: 2186585X
• ISSN: 00408735
• 本文言語コード: en
• データソース種別:
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  • Crossref
  • CiNii Articles
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• 抄録ライセンスフラグ: 使用不可