Skeletal examination in a chick embryo model of fetal alcohol syndrome indicates impaired osteogenesis

Abstract

In this chapter, we study Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. In section 1, we study holomorphic Riemannian maps as a generalization of holomorphic submersions and obtain a characterization of such maps. In section 2, we investigate anti-invariant Riemannian maps as a generalization of anti-invariant submersion, investigate the geometry of leaves of distributions defined by such maps, and give necessary and sufficient conditions for anti-invariant Riemannian maps to be totally geodesic. We also find necessary and sufficient conditions for the total manifold of anti-invariant Riemannian maps to be an Einstein manifold. In section 3, as a generalization of the semi-invariant submersion, we introduce semi-invariant Riemannian maps, give examples, and obtain the main properties of such maps. In section 4, we introduce generic Riemannian maps from almost Hermitian manifolds to Riemannian manifolds as a generalization of generic submersions and we give examples. We also find new conditions for Riemannian maps to be totally geodesic and harmonic. In section 5, we study slant Riemannian maps as a generalization of slant submersion, give examples, and obtain the harmonicity of such maps. We also find new necessary and sufficient conditions for such maps to be totally geodesic. Moreover, we obtain a decomposition theorem by slant Riemannian maps. In section 6, we define semi-slant Riemannian maps and give examples. In section 7, we introduce hemi-slant Riemannian maps as a generalization of hemi-slant submersions and slant Riemannian maps, give examples, obtain integrability conditions for distribution, and investigate the geometry of these distributions. We also obtain conditions for such maps to be harmonic and totally geodesic, respectively.