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

  • Amalendu Ghosh
  • Ramesh Sharma
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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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