Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and Riemannian maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds and K\"{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore’s classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, and extends their use in Riemannian maps. The work obtains new properties of the domain manifolds and target manifolds, and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps. Systematically reviews and references modern literature in Riemannian maps.Self-contained presentation supported by background information and references. Rigorous mathematical theory with applications discussed in chapter length.Accessible reading style with motivating examples helping the reader progress swiftly.