Pointwise hemi bi-slant submersions

In this study, we introduce a new notion of pointwise hemi bi-slant Riemannian submersions, a profound generalization encompassing various established submersion types like anti-invariant, slant, semi-slant, pointwise slant, pointwise semi-slant, and bi-slant submersions, all within the framework of almost product manifolds. After presenting a unique illustrative example, our investigation delves into the integrability conditions and geodesics governing this novel submersion concept. Furthermore, we unravel the complexities of ?-pluriharmonicity and ?-invariance within this context, revealing the subtle interplay between pointwise hemi bi-slant submersions? fibers and their classification as either geodesic or mixed geodesic. This in-depth analysis provides valuable insights into the intricate geometric properties of these fascinating mappings, offering a comprehensive understanding of their underlying principles and paving the way for future research and application.