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    ON THE BEHAVIOUR OF TOTAL UMBILICAL FIBERS UNDER QUARTER-SYMMETRIC NON-METRIC CONNECTIONS IN RIEMANNIAN SUBMERSIONS
    (Editura Bibliotheca-Bibliotheca Publ House, 2025) Karatas, Esra; Zeren, Semra; Altin, Mustafa
    In this study, we investigate the geometric properties of Riemannian submersions endowed with quarter-symmetric non-metric connections. We focus specifically on the M-projective curvature tensor and the conformal curvature tensor, providing an analysis of the behaviour of these tensors. We emphasize how these curvature tensors interact with totally umbilical fibers in the setting of Riemannian submersions. We explicitly compute the relevant curvature tensors and examine how the totally umbilical condition influences their relations. This clarifies the connections among the tensors and shows how they affect the geometric structure of the submersions.
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    RIEMANNIAN SUBMERSIONS ENDOWED WITH A NEW TYPE OF SEMI-SYMMETRIC NON-METRIC CONNECTION
    (Vinca Inst Nuclear Sci, 2023) Karatas, Esra; Zeren, Semra; Altin, Mustafa
    In this paper we study relations for the covariant derivative of O'Neill's tensor fields, Riemannian curvature, Ricci curvature and scalar curvature of the Riemannian submersion from a Riemannian manifold with respect to a new type of semi-symmetric non-metric connection to a Riemannian manifold, respectively, and demonstrate the relationship between them.