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Transversal Jacobi Operators in Almost Contact Manifolds

Author

Listed:
  • Jong Taek Cho

    (Department of Mathematics, Chonnam National University, Gwangju 61186, Korea)

  • Makoto Kimura

    (Department of Mathematics, Faculty of Science, Ibaraki University, Mito, Ibaraki 310-8512, Japan)

Abstract

Along a transversal geodesic γ whose tangent belongs to the contact distribution D , we define the transversal Jacobi operator R γ = R ( · , γ ˙ ) γ ˙ on an almost contact Riemannian manifold M . Then, using the transversal Jacobi operator R γ , we give a new characterization of the Sasakian sphere. In the second part, we characterize the complete ruled real hypersurfaces in complex hyperbolic space.

Suggested Citation

  • Jong Taek Cho & Makoto Kimura, 2020. "Transversal Jacobi Operators in Almost Contact Manifolds," Mathematics, MDPI, vol. 9(1), pages 1-9, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:31-:d:467872
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