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    • Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds

      Bayram Sahin

      Volume 118 Issue 4 November 2008 pp 573-581

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/118/04/0573-0581

    • Keywords

       

      Kaehler manifold; Sasakian manifold; locally conformal Kaehler manifold; harmonic map, Riemannian map; holomorphic map.

    • 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.

    • Author Affiliations

       

      Bayram Sahin1

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

    • Dates

       
      Published
      November 2008
      Manuscript received
      14 May 2007
      Manuscript revised
      4 December 2007

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