The Long-Time Behavior of the Ricci Tensor under the Ricci Flow. (19th September 2013)

• Record Type: Journal Article
• Authors: Hilaire, Christian
• Other Names: Calvaruso Giovanni Academic Editor.
• Is Part Of: Geometry. Volume 2013(2013)
• Publication Date: 2013-09-19
• Subjects: Geometry -- Periodicals; Geometry; Periodicals; 516
• DOI: 10.1155/2013/235436
• Languages: English
• ISSNs: 2314-422X

Abstract

Abstract : We show that, given an immortal solution to the Ricci flow on a closed manifold with uniformly bounded curvature and diameter, the Ricci tensor goes to zero as t → ∞ . We also show that if there exists an immortal solution on a closed 3-dimensional manifold such that the product of the curvature and the square of the diameter is uniformly bounded, then this solution must be of type III.