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Non-existence of harmonic maps on trans-Sasakian manifolds

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Abstract

In this paper, we have studied harmonic maps on trans-Sasakian manifolds. First it is proved that if F: M 1 → M 2 is a Riemannian ϕ-holomorphic map between two trans-Sasakian manifolds such that ξ 2 ∈ (Im dF)⊥, then F can not be harmonic provided that β 2 ≠ 0. We have also found the necessary and sufficient condition for the harmonic map to be constant map from Kaehler to trans-Sasakian manifold. Finally, we prove the non-existence of harmonic map from locally conformal Kaehler manifold to trans-Sasakian manifold.

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Authors and Affiliations

  1. Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, India

    A. J. P. Jaiswal & B. Avdhesh Pandey

  2. Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, India

    A. J. P. Jaiswal & B. Avdhesh Pandey

Authors
  1. A. J. P. Jaiswal
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  2. B. Avdhesh Pandey
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Correspondence to A. J. P. Jaiswal.

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Submitted by M. A. Malakhaltsev

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Jaiswal, A.J.P., Pandey, B.A. Non-existence of harmonic maps on trans-Sasakian manifolds. Lobachevskii J Math 37, 185–192 (2016). https://doi.org/10.1134/S1995080216020074

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  • DOI: https://doi.org/10.1134/S1995080216020074

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