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The critical point equation and contact geometry

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Abstract

In this paper, we consider the CPE conjecture in the frame-work of \({K}\)-contact manifold and \({(\kappa, \mu)}\)-contact manifold. First, we prove that a complete \({K}\)-contact metric satisfying the CPE is Einstein and is isometric to a unit sphere \({S^{2n+1}}\). Next, we prove that if a non-Sasakian \({ (\kappa, \mu) }\)-contact metric satisfies the CPE, then \({ M^{3} }\) is flat and for \({ n > 1 }\), \({ M^{2n+1} }\) is locally isometric to \({ E^{n+1} \times S^{n}(4)}\).

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Authors and Affiliations

  1. Department of Mathematics, Chandernagore College, Hooghly, 712 136, West Bengal, India

    Amalendu Ghosh

  2. Department of Mathematics, Jadavpur University, 188 Raja S. C. Mullick Road, Kolkata, 700 032, India

    Dhriti Sundar Patra

Authors
  1. Amalendu Ghosh
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  2. Dhriti Sundar Patra
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Correspondence to Amalendu Ghosh.

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Ghosh, A., Patra, D.S. The critical point equation and contact geometry. J. Geom. 108, 185–194 (2017). https://doi.org/10.1007/s00022-016-0333-3

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  • DOI: https://doi.org/10.1007/s00022-016-0333-3

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