Anzeige
Erschienen in:
2011 | OriginalPaper | Buchkapitel
The Cone Construction of Böhm and Wilking
verfasst von : Ben Andrews, Christopher Hopper
Erschienen in: The Ricci Flow in Riemannian Geometry
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.