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Evolution of the Curvature

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Date

2011

Authors

Andrews, Ben
Hopper, Christopher

Journal Title

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Volume Title

Publisher

Springer Verlag

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Research Projects

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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.

Description

Keywords

Bianchi Identity, Civita Connection, Curvature Tensor, Ricci Flow, Riemannian Manifold

Citation

URI

https://hdl.handle.net/1885/733798133

Collections

ANU Research Publications

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Type

Book chapter

Book Title

The Ricci Flow in Riemannian Geometry: A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem

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Publication

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DOI

10.1007/978-3-642-16286-2_4

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