Skip to main content

The Cone Construction of Böhm and Wilking

  • 2782 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 2011)

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

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   49.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   64.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ben Andrews .

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

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

Download citation