The Manifolds with Ricci Curvature Decay to Zero

• 作者: Huashui Zhan
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Cheeger-Gromoll Theorem Busemann Function Complete RIEMANNIAN MANIFOLD RICCI Curvature DECAY to ZERO
• 年，卷（期）: 2012,（1）
• 页码范围: 36-38
• 页数: 3页
• 分类号: O1

摘要

The paper quotes the concept of Ricci curvature decay to zero. Base on this new concept, by modifying the proof of the canonical Cheeger-Gromoll Splitting Theorem, the paper proves that for a complete non-compact Riemannian manifold M with Ricci curvature decay to zero, if there is a line in M, then the isometrically splitting M = R × N is true.