Nguyen, H. T. (2009) Isotropic curvature and the ricci flow. International Mathematics Research Notices, Vol.2012 (No.3). pp. 536-558. doi:10.1093/imrn/rnp147 ISSN 1073-7928.

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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.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	International Mathematics Research Notices
Publisher:	Oxford University Press
ISSN:	1073-7928
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.2012
Number:	No.3
Page Range:	pp. 536-558
DOI:	10.1093/imrn/rnp147
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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