Abstract
If a non-Sasakian (k, μ)-contact metric g is a non-trivial Ricci soliton on a (2n + 1)-dimensional smooth manifold M, then (M, g) is locally a three-dimensional Gaussian soliton, or a gradient shrinking rigid Ricci soliton on the trivial sphere bundle S n(4) × E n+1, or a non-gradient expanding Ricci soliton with \(k = 0,\mu = 4\). The last case occurs on a Lie group with a left invariant metric, especially for dimension 3, on Sol 3 regarded also as the group E(1, 1) of rigid motions of the Minkowski 2-space.
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Acknowledgements
We thank Professor Peter Petersen for help on a particular issue. R.S. was supported by the University of New Haven Research Scholarship.
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Ghosh, A., Sharma, R. (2014). A Classification of Ricci Solitons as (k, μ)-Contact Metrics. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_31
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