Isotropic Curvature and the Ricci Flow

Nguyen, Huy T.

doi:10.1093/imrn/rnp147

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Isotropic Curvature and the Ricci Flow

MPS-Authors

/persons/resource/persons2715

Nguyen, Huy T.
Geometric Analysis and Gravitation, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

rnp147v1.pdf
(Any fulltext), 172KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Nguyen, H. T. (2010). Isotropic Curvature and the Ricci Flow. International Mathematics Research Notices, 2010(3): rnp147, pp. 536-558. doi:10.1093/imrn/rnp147.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-9DDC-9

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.