Pointwise Semislant Riemannian Maps Into Almost Hermitian Manifolds and Casorati Inequalities

As a natural generalization of slant submanifolds [B.-Y. Chen, Bull. Austral. Math. Soc.,41, No. 1, 135 (1990)], slant submersions [B. & Scedil;ahin, Bull. Math. Soc. Sci. Math. Roumanie (N.S.),54, No. 102, 93 (2011)], slant Riemannian maps [B. & Scedil;ahin, Quaestion. Math.,36, No. 3, 449 (2013) and Int. J. Geom. Meth. Mod. Phys.,10, Article 1250080 (2013)], pointwise slant submanifolds [B.-Y. Chen and O. J. Garay, Turkish J. Math.,36, 630 (2012)], pointwise slant submersions [J. W. Lee and B. , Sahin, Bull. Korean Math. Soc.,51, No. 4, 1115 (2014)], pointwise slant Riemannian maps [Y. G & uuml;nd & uuml;zalp and M. A. Akyol, J. Geom. Phys.,179, Article 104589 (2022)], semislant submanifolds [N. Papaghiuc, Ann. & Scedil;tiin & tcedil;. Univ. Al. I. Cuza Ia & scedil;i. Mat. (N.S.),40, 55 (1994)], semislant submersions [K.-S. Park and R. Prasad, Bull. Korean Math. Soc.,50, No. 3, Article 951962 (2013)], and semislant Riemannian maps [K.-S. Park and B. , Sahin, Czechoslovak Math. J.,64, No. 4, 1045 (2014)], we introduce a new class of Riemannian maps, which are called pointwise semislant Riemannian maps, from Riemannian manifolds to almost Hermitian manifolds. First, we present some examples, propose a characterization, and obtain the geometry of foliations in terms of the distributions involved in the definition of these maps. We also establish necessary and sufficient conditions for the pointwise semislant Riemannian maps to be totally geodesic and harmonic, respectively. Finally, we determine the Casorati curvatures for pointwise semislant Riemannian maps in the complex space form.