Abstract
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.
Highlights
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, the isometrically splitting M = R × N is true
The proof of Cheeger-Gromoll Splitting Theorem is based on the sub-harmonicity of the Busemann functions, we will give some details in what follows
Summary
Gromoll [1] proved the following classical: Cheeger-Gromoll Splitting Theorem: Let M be a complete Riemannian manifold with. If there is a line in M, the isometrically splitting M R N is true. The proof of Cheeger-Gromoll Splitting Theorem is based on the sub-harmonicity of the Busemann functions, we will give some details in what follows. Let M be a noncompact complete Riemannian manifold and
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
