The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting; theorem is generalized. They also stu...The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting; theorem is generalized. They also study topology of such manifolds.展开更多
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 Riem...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.展开更多
文摘The authors study complete open manifolds whose curvature is non-negative along ray directions. They prove that such manifold has infinite volume. Cheeger-Gromoll's splitting; theorem is generalized. They also study topology of such manifolds.
文摘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.
