Analysis of Total Umbilical Fibers in Riemannian Submersions with Quarter Symmetric Non-Metric Connections

In this study, we examine the geometric properties of Riemannian submersions with quarter symmetric non-metric connections. Our work provides a compre-hensive analysis of the Weyl projective curvature tensor, the concircular curvature tensor, and the conharmonic curvature tensor. We also investigate how these curvature tensors interact with the total umbilic fibers, particularly focusing on their behavior when such fibers are present in Riemannian submersions. First we introduce basic properties of quarter symmetric non-metric connections. Subse-quently, we compute the relevant curvature tensors and analyze their interplay with total umbilic fibers. In this context, we elucidate relationships between var-ious curvature tensors and certain geometric properties, as well as the effects of these relationships on Riemannian submersions.