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Metric f-Contact Manifolds Satisfying the (κ, μ)-Nullity Condition
Mathematics ( IF 2.3 ) Pub Date : 2020-06-02 , DOI: 10.3390/math8060891
Alfonso Carriazo , Luis M. Fernández , Eugenia Loiudice

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.

中文翻译:

满足(κ,μ)-零条件的度量f-接触流形

我们证明如果f截面曲率在a的任何点 2 ñ + s 尺寸的f接触流形满足 κ μ 具有的无效条件 ñ > 1个 与点的f截面无关,则在流形上恒定。此外,我们还证明了一个非正常指标˚F -接触歧管满足 κ μ 当且仅当以下情况时,无效条件具有恒定的f截面曲率: μ = κ + 1个 在这种情况下,我们给出了曲率张量场的显式表达式。最后,我们给出一些例子。
更新日期:2020-06-02
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