Abstract
We study the asymptotic behavior of the normalized Ricci flow on generalized Wallach spaces that could be considered as a special planar dynamical system. All nonsymmetric generalized Wallach spaces can be naturally parametrized by three positive numbers \(a_{1},a_{2},a_{3}\). Our interest is to determine the type of singularity of all singular points of the normalized Ricci flow on all such spaces. Our main result gives a qualitative answer for almost all points \((a_{1},a_{2},a_{3})\) in the cube \((0,1/2] \times (0,1/2] \times (0,1/2]\). We also consider in detail some important partial cases.
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Acknowledgements
The authors are indebted to Prof. Yusuke Sakane for useful discussions concerning computational aspects of this project and to Tanya Nikonorova for her help with the graphics. The project was supported in part by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (grant NSh-921.2012.1) and by Federal Target Grant “Scientific and educational personnel of innovative Russia” for 2009–2013 (agreement no. 8206, application no. 2012-1.1-12-000-1003-014).
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Abiev, N.A., Arvanitoyeorgos, A., Nikonorov, Y.G., Siasos, P. (2014). The Ricci Flow on Some Generalized Wallach Spaces. In: Rovenski, V., Walczak, P. (eds) Geometry and its Applications. Springer Proceedings in Mathematics & Statistics, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-319-04675-4_1
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DOI: https://doi.org/10.1007/978-3-319-04675-4_1
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