Abstract
In this section the remarkable formulas derived in the previous section, particularly the identities (12.13) and (12.14), will be applied to construct a family of cones preserved by the Ricci flow. We follow the argument presen- ted by Böhm and Wilking who applied it to produce a family of preserved cones interpolating between the cone of positive curvature operators and the line of constant positive curvature operators. The construction applies much more generally, so that given any preserved cone satisfying a few conditions, there is a family of cones linking that one to the ray of constant positive curvature operators. As we will see, this is a crucial step in proving that solutions the Ricci flow converge to spherical space forms.
Keywords
- Scalar Curvature
- Ricci Curvature
- Tangent Cone
- Closed Convex Cone
- Ricci Flow
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© 2011 Springer-Verlag Berlin Heidelberg
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Andrews, B., Hopper, C. (2011). The Cone Construction of Böhm and Wilking. 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_13
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DOI: https://doi.org/10.1007/978-3-642-16286-2_13
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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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