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A generalization of K-contact and (k, μ)-contact manifolds

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Abstract

We study a generalization of K-contact and (k, μ)-contact manifolds, and show that if such manifolds of dimensions ≥ 5 are conformally flat, then they have constant curvature +1. We also show under certain conditions that such manifolds admitting a non-homothetic closed conformal vector field are isometric to a unit sphere. Finally, we show that such manifolds with parallel Ricci tensor are either Einstein, or of zero \({\xi}\)-sectional curvature.

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Authors and Affiliations

  1. Department of Mathematics, Krishnagar Government College, Krishnanagar, 741101, West Bengal, India

    Amalendu Ghosh

  2. Department of Mathematics, University of New Haven, West Haven, CT, 06516, USA

    Ramesh Sharma

Authors
  1. Amalendu Ghosh
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  2. Ramesh Sharma
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Correspondence to Ramesh Sharma.

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Ghosh, A., Sharma, R. A generalization of K-contact and (k, μ)-contact manifolds. J. Geom. 103, 431–443 (2012). https://doi.org/10.1007/s00022-013-0144-8

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  • DOI: https://doi.org/10.1007/s00022-013-0144-8

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