1. CMB 2011 (vol 56 pp. 173)
|Semi-invariant Submersions from Almost Hermitian Manifolds|
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