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

ISBN-13: 9780128043912 / Angielski / Twarda / 2017 / 360 str.

Bayram Sahin

Opis

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 Khlerian 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.

• Systematically reviews and references modern literature in Riemannian maps
• Provides rigorous mathematical theory with applications
• Presented in an accessible reading style with motivating examples that help the reader rapidly progress

Recenzje

"This remarkable book is suitable for autostudy. It is a very nicely written book with important applications," --Zentralblatt MATH 1378

Spis treści

1. Basic Geometric Structures on Manifolds2. Applications of Riemannian Submersions3. Riemannian submersions From Almost Hermitian Manifolds4. Riemannian Maps5. Riemannian Maps From Almost Hermitian Manifolds6. Riemannian Maps To Almost Hermitian Manifolds