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A Note on Nearly Sasakian Manifolds

Author

Listed:
  • Fortuné Massamba

    (School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01, Scottsville 3209, South Africa)

  • Arthur Nzunogera

    (Centre de Recherche en Mathématiques et Physiques (CRMP), École Doctorale, Université du Burundi, Bujumbura P.O. Box 2700, Burundi
    École Normale Supérieure, Centre de Recherche en Sciences et de Perfectionnement Professionnel (CReSP), Bujumbura P.O. Box 6983, Burundi)

Abstract

A class of nearly Sasakian manifolds is considered in this paper. We discuss the geometric effects of some symmetries on such manifolds and show, under a certain condition, that the class of Ricci semi-symmetric nearly Sasakian manifolds is a subclass of Einstein manifolds. We prove that a Codazzi-type Ricci nearly Sasakian space form is either a Sasakian manifold with a constant ϕ -holomorphic sectional curvature H = 1 or a 5-dimensional proper nearly Sasakian manifold with a constant ϕ -holomorphic sectional curvature H > 1 . We also prove that the spectrum of the operator H 2 generated by the nearly Sasakian space form is a set of a simple eigenvalue of 0 and an eigenvalue of multiplicity 4, and we induce that the underlying space form carries a Sasaki–Einstein structure. We show that there exist integrable distributions with totally geodesic leaves on the same manifolds, and we prove that there are no proper nearly Sasakian space forms with constant sectional curvature.

Suggested Citation

  • Fortuné Massamba & Arthur Nzunogera, 2023. "A Note on Nearly Sasakian Manifolds," Mathematics, MDPI, vol. 11(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2634-:d:1167286
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    Cited by:

    1. Vladimir Rovenski, 2023. "Weak Nearly Sasakian and Weak Nearly Cosymplectic Manifolds," Mathematics, MDPI, vol. 11(20), pages 1-10, October.

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