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Metric f -Contact Manifolds Satisfying the ( κ , μ )-Nullity Condition

Author

Listed:
  • Alfonso Carriazo

    (Departamento de Geometría y Topología, c/Tarfia s/n, Universidad de Sevilla, 41012 Sevilla, Spain
    These authors contributed equally to this work.)

  • Luis M. Fernández

    (Departamento de Geometría y Topología, c/Tarfia s/n, Universidad de Sevilla, 41012 Sevilla, Spain
    These authors contributed equally to this work.)

  • Eugenia Loiudice

    (Fachbereich Mathematik und Informatik, Philipps Universität Marburg, Hans-Meerwein-Straße, 35032 Marburg, Germany
    These authors contributed equally to this work.)

Abstract

We prove that if the f -sectional curvature at any point of a ( 2 n + s ) -dimensional metric f -contact manifold satisfying the ( κ , μ ) nullity condition with n > 1 is independent of the f -section at the point, then it is constant on the manifold. Moreover, we also prove that a non-normal metric f -contact manifold satisfying the ( κ , μ ) nullity condition is of constant f -sectional curvature if and only if μ = κ + 1 and we give an explicit expression for the curvature tensor field in such a case. Finally, we present some examples.

Suggested Citation

  • Alfonso Carriazo & Luis M. Fernández & Eugenia Loiudice, 2020. "Metric f -Contact Manifolds Satisfying the ( κ , μ )-Nullity Condition," Mathematics, MDPI, vol. 8(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:891-:d:366164
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