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Harmonic Riemannian maps on locally conformal Kaehler manifolds

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Abstract

We study harmonic Riemannian maps on locally conformal Kaehler manifolds (lcK manifolds). We show that if a Riemannian holomorphic map between lcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the lcK manifold is Kaehler. Then we find similar results for Riemannian maps between lcK manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.

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Authors and Affiliations

  1. Department of Mathematics, Inonu University, 44280, Malatya, Turkey

    Bayram Sahin

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  1. Bayram Sahin
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Correspondence to Bayram Sahin.

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Sahin, B. Harmonic Riemannian maps on locally conformal Kaehler manifolds. Proc Math Sci 118, 573–581 (2008). https://doi.org/10.1007/s12044-008-0045-1

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  • DOI: https://doi.org/10.1007/s12044-008-0045-1

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