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Ricci flow and manifolds with positive curvature

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Symmetry: Representation Theory and Its Applications

Part of the book series: Progress in Mathematics ((PM,volume 257))

Abstract

This is an expository article based on the author’s lecture delivered at the conference Lie Theory and Its Applications in March 2011, UCSD. We discuss various notions of positivity and their relations with the study of the Ricci flow, including a proof of the assertion, due to Wolfson and the author, that the Ricci flow preserves the positivity of the complex sectional curvature. We discuss the examples of Wallach of the manifolds with positive pinched sectional curvature and the behavior of Ricci flow on some examples. Finally we discuss the recent joint work with Wilking on the manifolds with pinched flag curvature and some open problems.

The research of the author was partially supported by NSF grant DMS-1105549.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093, USA

    Lei Ni

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  1. Lei Ni
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Correspondence to Lei Ni .

Editor information

Editors and Affiliations

  1. Dept. Mathematics 442 Dunham Lab, Yale University, New Haven, Connecticut, USA

    Roger Howe

  2. Department of Mathematics, Baylor University, Waco, Texas, USA

    Markus Hunziker

  3. Department of Mathematical Sciences EMS Building, Room E403, University of Wisconsin, Milwaukee, Milwaukee, Wisconsin, USA

    Jeb F. Willenbring

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Dedicated to Nolan Wallach on his 70th birthday

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Ni, L. (2014). Ricci flow and manifolds with positive curvature. In: Howe, R., Hunziker, M., Willenbring, J. (eds) Symmetry: Representation Theory and Its Applications. Progress in Mathematics, vol 257. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-1590-3_17

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