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Turkish Journal of Mathematics

Author ORCID Identifier

BERAN PİRİNÇÇİ: 0000-0002-4692-9590

ÇAĞRIHAN ÇİMEN: 0009-0000-6331-9615

DENİZ ULUSOY: 0000-0002-0742-4047

HAKAN METE TAŞTAN: 0000-0002-0773-9305

Abstract

We give a characterization theorem for a globally conformal Kenmotsu manifold with an illustrative example. Then we study Riemannian, antiinvariant and Lagrangian submersions from globally conformal Kenmotsu manifolds. Initially, we show that the gradient vector field of the conformal transformation and the Lee vector field of the total manifold of a Riemannian submersion is horizontal when the characteristic vector field is a horizontal vector field. We give necessary and sufficient conditions for the integrability and totally geodesicness of vertical and horizontal distributions of antiinvariant and Lagrangian submersions whose total manifolds are globally conformal Kenmotsu. We also give a necessary and sufficient condition for the harmonicity of an antiinvariant Riemannian submersion whose total manifold is globally conformal Kenmotsu. Finally, we study the condition for a curve in a Lagrangian submersion whose total manifold is globally conformal Kenmotsu to be geodesic, and derive a criterion for such submersions to be Clairaut submersions. In that case, we show that if the dimension of the base manifold is at least two less than the dimension of the total manifold, then the characteristic vector field must be horizontal.

DOI

10.55730/1300-0098.3676

Keywords

Riemannian submersion, Lagrangian submersion, globally conformal structure, Kenmotsu manifold

First Page

690

Last Page

708

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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