We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semi-invariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.

Keywords:

Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion

MSC Classifications:

53B20, 53C43 show english descriptions Local Riemannian geometry
Differential geometric aspects of harmonic maps [See also 58E20] 53B20 - Local Riemannian geometry
53C43 - Differential geometric aspects of harmonic maps [See also 58E20]

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