• Title/Summary/Keyword: (${\kappa},{\mu}$)-paracontact manifold

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CHARACTERIZATIONS FOR TOTALLY GEODESIC SUBMANIFOLDS OF (𝜅, 𝜇)-PARACONTACT METRIC MANIFOLDS

  • Atceken, Mehmet;Uygun, Pakize
    • Korean Journal of Mathematics
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    • v.28 no.3
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    • pp.555-571
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    • 2020
  • The aim of the present paper is to study pseudoparallel invariant submanifold of a (𝜅, 𝜇)-paracontact metric manifold. We consider pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci generalized pseudo parallel invariant submanifolds of a (𝜅, 𝜇)-paracontact metric manifold and we obtain new results contribute to geometry.

The Geometry of 𝛿-Ricci-Yamabe Almost Solitons on Paracontact Metric Manifolds

  • Somnath Mondal;Santu Dey;Young Jin Suh;Arindam Bhattacharyya
    • Kyungpook Mathematical Journal
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    • v.63 no.4
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    • pp.623-638
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    • 2023
  • In this article we study a 𝛿-Ricci-Yamabe almost soliton within the framework of paracontact metric manifolds. In particular we study 𝛿-Ricci-Yamabe almost soliton and gradient 𝛿-Ricci-Yamabe almost soliton on K-paracontact and para-Sasakian manifolds. We prove that if a K-paracontact metric g represents a 𝛿-Ricci-Yamabe almost soliton with the non-zero potential vector field V parallel to 𝜉, then g is Einstein with Einstein constant -2n. We also show that there are no para-Sasakian manifolds that admit a gradient 𝛿-Ricci-Yamabe almost soliton. We demonstrate a 𝛿-Ricci-Yamabe almost soliton on a (𝜅, 𝜇)-paracontact manifold.