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Weak Nearly Sasakian and Weak Nearly Cosymplectic Manifolds

Author

Listed:
  • Vladimir Rovenski

    (Department of Mathematics, University of Haifa, Haifa 3498838, Israel)

Abstract

Weak contact metric structures on a smooth manifold, introduced by V. Rovenski and R. Wolak in 2022, have provided new insight into the theory of classical structures. In this paper, we define new structures of this kind (called weak nearly Sasakian and weak nearly cosymplectic and nearly Kähler structures), study their geometry and give applications to Killing vector fields. We introduce weak nearly Kähler manifolds (generalizing nearly Kähler manifolds), characterize weak nearly Sasakian and weak nearly cosymplectic hypersurfaces in such Riemannian manifolds and prove that a weak nearly cosymplectic manifold with parallel Reeb vector field is locally the Riemannian product of a real line and a weak nearly Kähler manifold.

Suggested Citation

  • Vladimir Rovenski, 2023. "Weak Nearly Sasakian and Weak Nearly Cosymplectic Manifolds," Mathematics, MDPI, vol. 11(20), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4377-:d:1264505
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    References listed on IDEAS

    as
    1. Sharief Deshmukh & Olga Belova, 2021. "On Killing Vector Fields on Riemannian Manifolds," Mathematics, MDPI, vol. 9(3), pages 1-17, January.
    2. Fortuné Massamba & Arthur Nzunogera, 2023. "A Note on Nearly Sasakian Manifolds," Mathematics, MDPI, vol. 11(12), pages 1-20, June.
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    Cited by:

    1. Vladimir Rovenski, 2024. "Weak Quasi-Contact Metric Manifolds and New Characteristics of K-Contact and Sasakian Manifolds," Mathematics, MDPI, vol. 12(20), pages 1-9, October.

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