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 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, also extending their use in Riemannian maps.

The work obtains new properties of the domain 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.

Submersii Riemanniene, Harti Riemanniene in Geometria Hermitiana si aplicatiile lor este o expunere bogata si autonoma a dezvoltarilor recente in submersiuni si harti Riemanniene relevante pentru geometria complexa, concentrandu-se in special pe submersiuni noi, varietati hermitiene si varietati K {a} hleriene. Scufundarile Riemanniene au fost mult timp un instrument eficient pentru a obtine noi varietati si a compara anumite varietati in cadrul geometriei diferentiale.