Pointwise hemi-slant Riemannian maps ($\mathcal{PHSRM}$) from almost Hermitian manifolds

In 2022, the notion of pointwise slant Riemannian maps were introduced by Y. Gündüzalp and M. A. Akyol in [J. Geom. Phys. {179}, 104589, 2022] as a natural generalization of slant Riemannian maps, slant Riemannian submersions, slant submanifolds. As a generalization of pointwise slant Riemannian maps and many subclasses notions, we introduce pointwise hemi-slant Riemannian maps (briefly, $\mathcal{PHSRM}$) from almost Hermitian manifolds to Riemannian manifolds, giving a figure which shows the subclasses of the map and a non-trivial (proper) example and investigate some properties of the map, we deal with their properties: the J-pluriharmonicity, the J-invariant, and the totally geodesicness of the map. Finally, we study some curvature relations in complex space form, involving Chen inequalities and Casorati curvatures for $\mathcal{PHSRM}$, respectively.