$\phi-$pluriharmonicity and $\phi-$invariance of pointwise hemi bi-slant submersions

Abstract

In this study, we embark on an exploration of the intricate domain 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 $\phi-$pluriharmonicity and $\phi-$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.