Sahin, Bayram2024-08-042024-08-0420110219-88781793-6977https://doi.org/10.1142/S0219887811005725https://hdl.handle.net/11616/95523This paper has two aims. First, we show that the usual notion of umbilical maps between Riemannian manifolds does not work for Riemannian maps. Then we introduce a new notion of umbilical Riemannian maps between Riemannian manifolds and give a method on how to construct examples of umbilical Riemannian maps. In the second part, as a generalization of CR-submanifolds, holomorphic submersions, anti-invariant submersions, invariant Riemannian maps and anti-invariant Riemannian maps, we introduce semi-invariant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds, give examples and investigate the geometry of distributions which are arisen from definition. We also obtain a decomposition theorem and give necessary and sufficient conditions for a semi-invariant Riemannian map to be totally geodesic. Then we study the geometry of umbilical semi-invariant Riemannian maps and obtain a classification theorem for such Riemannian maps.eninfo:eu-repo/semantics/closedAccessRiemannian mapsemi-invariant Riemannian mapisometric immersionRiemannian submersioninvariant Riemannian mapanti-invariant Riemannian mapArticle871439145410.1142/S02198878110057252-s2.0-84555178382Q3WOS:000298384100003Q3