Isotropic curvature and the Ricci flow

Nguyen, Huy T. (2010) Isotropic curvature and the Ricci flow. International Mathematics Research Notices, 3: 536-558. doi:10.1093/imrn/rnp147

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Author Nguyen, Huy T.
Title Isotropic curvature and the Ricci flow
Journal name International Mathematics Research Notices   Check publisher's open access policy
ISSN 1073-7928
Publication date 2010-01-01
Sub-type Article (original research)
DOI 10.1093/imrn/rnp147
Issue 3
Start page 536
End page 558
Total pages 23
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Language eng
Abstract In this paper, we study the Ricci flow on higher dimensional compact manifolds. We prove that nonnegative isotropic curvature is preserved by the Ricci flow in dimensions greater than or equal to four. In order to do so, we introduce a new technique to prove that curvature functions defined on the orthonormal frame bundle are preserved by the Ricci flow. At a minimum of such a function, we compute the first and second derivatives in the frame bundle. Using an algebraic construction, we can use these expressions to show that the nonlinearity is positive at a minimum. Finally, using the maximum principle, we can show that the Ricci flow preserves the cone of curvature operators with nonnegative isotropic curvature.
Keyword Positive curvature
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 16 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 20 times in Scopus Article | Citations
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