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Ricci flow on homogeneous spaces with two isotropy summands

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Abstract

We consider the Ricci flow equation for invariant metrics on compact and connected homogeneous spaces whose isotropy representation decomposes into two irreducible inequivalent summands. By studying the corresponding dynamical system, we completely describe the behaviour of the homogeneous Ricci flow on this kind of spaces. Moreover, we investigate the existence of ancient solutions and relate this to the existence and non-existence of invariant Einstein metrics.

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Acknowledgments

This paper is part of my PhD thesis [10]. I would like to thank my supervisor Prof. Andrew Dancer for his current support and motivation and Chris Hopper, Prof. Ernesto Buzano and Prof. McKenzie Wang for useful discussions. I would also like to thank Prof. Lei Ni for bringing to my attention reference [2]. Finally, I would like to acknowledge the EPSRC and the Accademia delle Scienze di Torino for financial support.

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  1. Department of Mathematics and Statistics, McMaster University, 1280 Main street West, Hamilton, ON, L8S 4K1, Canada

    Maria Buzano

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  1. Maria Buzano
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Correspondence to Maria Buzano.

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Buzano, M. Ricci flow on homogeneous spaces with two isotropy summands. Ann Glob Anal Geom 45, 25–45 (2014). https://doi.org/10.1007/s10455-013-9386-9

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  • DOI: https://doi.org/10.1007/s10455-013-9386-9

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