Mohammed Y. Abass ; Habeeb M. Abood - Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type

cm:10869 - Communications in Mathematics, February 7, 2023, Volume 32 (2024), Issue 1 - https://doi.org/10.46298/cm.10869
Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu typeArticle

Authors: Mohammed Y. Abass ; Habeeb M. Abood

    This paper determined the components of the generalized curvature tensor for the class of Kenmotsu type and established the mentioned class is {\eta}-Einstein manifold when the generalized curvature tensor is flat; the converse holds true under suitable conditions. It also introduced the notion of generalized {\Phi}-holomorphic sectional (G{\Phi}SH-) curvature tensor and thus found the necessary and sufficient conditions for the class of Kenmotsu type to be of constant G{\Phi}SH-curvature. In addition, the notion of {\Phi}-generalized semi-symmetric was introduced and its relationship with the class of Kenmotsu type and {\eta}-Einstein manifold established. Furthermore, this paper generalized the notion of the manifold of constant curvature and deduced its relationship with the aforementioned ideas. It finally showed that the class of Kenmotsu type exists as a hypersurface of the Hermitian manifold and derived a relation between the components of the Riemannian curvature tensors of the almost Hermitian manifold and its hypersurfaces.


    Volume: Volume 32 (2024), Issue 1
    Published on: February 7, 2023
    Accepted on: January 30, 2023
    Submitted on: January 30, 2023
    Keywords: Mathematics - Differential Geometry

    Consultation statistics

    This page has been seen 154 times.
    This article's PDF has been downloaded 89 times.