A Classification of Ricci Solitons as (k, μ)-Contact Metrics

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


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.


Contact Manifold Ricci Soliton Sasakian Manifold Ricci Flow Ricci Operator 



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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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Chandernagore CollegeWest BengalIndia
  2. 2.University of New HavenWest HavenUSA

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