Evolution of the Curvature
| dc.contributor.author | Andrews, Ben | en |
| dc.contributor.author | Hopper, Christopher | en |
| dc.date.accessioned | 2025-12-31T21:41:27Z | |
| dc.date.available | 2025-12-31T21:41:27Z | |
| dc.date.issued | 2011 | en |
| dc.description.abstract | The Ricci flow is introduced in this chapter as a geometric heat-type equation for the metric. In Sect. 4.4 we derive evolution equations for the curvature, and its various contractions, whenever the metric evolves by Ricci flow. These equations, particularly that of Theorem 4.14, are pivotal to our analysis throughout the coming chapters. In Sect. 4.5.3 we discuss a historical re- sult concerning the convergence theory for the Ricci flow in n-dimensions. This will motivational much of the Böhm and Wilking analysis discussed in Chap. 11. | en |
| dc.description.status | Peer-reviewed | en |
| dc.format.extent | 20 | en |
| dc.identifier.isbn | 9783642159664 | en |
| dc.identifier.issn | 0075-8434 | en |
| dc.identifier.other | ORCID:/0000-0002-6507-0347/work/162948208 | en |
| dc.identifier.scopus | 85072849848 | en |
| dc.identifier.uri | https://hdl.handle.net/1885/733798133 | |
| dc.language.iso | en | en |
| dc.publisher | Springer Verlag | en |
| dc.relation.ispartof | The Ricci Flow in Riemannian Geometry: A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem | en |
| dc.relation.ispartofseries | Lecture Notes in Mathematics | en |
| dc.rights | Publisher Copyright: © 2011, Springer-Verlag Berlin Heidelberg. | en |
| dc.subject | Bianchi Identity | en |
| dc.subject | Civita Connection | en |
| dc.subject | Curvature Tensor | en |
| dc.subject | Ricci Flow | en |
| dc.subject | Riemannian Manifold | en |
| dc.title | Evolution of the Curvature | en |
| dc.type | Book chapter | en |
| dspace.entity.type | Publication | en |
| local.bibliographicCitation.lastpage | 82 | en |
| local.bibliographicCitation.startpage | 63 | en |
| local.contributor.affiliation | Andrews, Ben; Mathematical Sciences Institute Research, Mathematical Sciences Institute, ANU College of Systems and Society, The Australian National University | en |
| local.contributor.affiliation | Hopper, Christopher; University of Oxford | en |
| local.identifier.doi | 10.1007/978-3-642-16286-2_4 | en |
| local.identifier.essn | 1617-9692 | en |
| local.identifier.pure | 4d630ace-4457-419c-b589-085bfe0ab680 | en |
| local.identifier.url | https://www.scopus.com/pages/publications/85072849848 | en |
| local.type.status | Published | en |