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Horizontally Conformal Submersions from CR-Submanifolds of Locally Conformal Kähler Manifolds

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Abstract

In this paper, we study horizontally conformal submersions from CR-submanifolds of a locally conformal Kähler manifold onto almost Hermitian manifolds, generalizing the results obtained by Şahin (Kodai Math. J. 31, 2008), for horizontally conformal submersions of CR-submanifolds in Kähler ambient space. In particular, we show that any horizontally homothetic submersion of a CR-submanifold M of a locally conformal Kähler manifold with Lee vector field normal to M is a Riemannian submersion up to a scale. Moreover, we obtain that such a map is harmonic, provided that the CR-submanifold is mixed geodesic.

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Acknowledgements

The author is extremely grateful to Professor Liviu Ornea for useful suggestions and remarks on the first draft of the paper and also to the referees for their thoughtful and thorough reviews. This work was supported by National Research Council—Executive Agency for Higher Education Research and Innovation Funding (CNCS-UEFISCDI), project number PN-III-P4-ID-PCE-2016-0065.

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  1. Research Center in Geometry, Topology and Algebra, University of Bucharest, Str. Academiei, Nr. 14, Sector 1, Bucureşti, 70109, Romania

    Gabriel-Eduard Vîlcu

  2. Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti, Nr. 39, Ploieşti, 100680, Romania

    Gabriel-Eduard Vîlcu

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Vîlcu, GE. Horizontally Conformal Submersions from CR-Submanifolds of Locally Conformal Kähler Manifolds. Mediterr. J. Math. 17, 26 (2020). https://doi.org/10.1007/s00009-019-1461-4

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