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Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds

Author

Listed:
  • Yanlin Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
    These authors contributed equally to this work.)

  • M. S. Siddesha

    (Department of Data Analytics and Mathematical Science, Jain (Deemed to be University), Global Campus, Bangalore 562112, India
    These authors contributed equally to this work.)

  • H. Aruna Kumara

    (Department of Mathematics, BMS Institute of Technology and Management, Yelahanka, Bangalore 560064, India
    These authors contributed equally to this work.)

  • M. M. Praveena

    (Department of Mathematics, M. S. Ramaiah Institute of Technology, Bangalore 560054, India
    These authors contributed equally to this work.)

Abstract

In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric ω -connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric ω -connection with a parallel Cotton tensor is quasi-Einstein and Bach flat. Next, we show that any quasi-Einstein Lorentzian manifold admitting a semi-symmetric metric ω -connection is Bach flat.

Suggested Citation

  • Yanlin Li & M. S. Siddesha & H. Aruna Kumara & M. M. Praveena, 2024. "Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds," Mathematics, MDPI, vol. 12(19), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3130-:d:1493353
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    References listed on IDEAS

    as
    1. Adela Mihai & Ion Mihai, 2018. "Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature," Mathematics, MDPI, vol. 6(3), pages 1-8, March.
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