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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Andrews, B., Hopper, C. (2011). Evolution of the Curvature. In: The Ricci Flow in Riemannian Geometry. Lecture Notes in Mathematics(), vol 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16286-2_4
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DOI: https://doi.org/10.1007/978-3-642-16286-2_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16285-5
Online ISBN: 978-3-642-16286-2
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