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.

• 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

Auteur

Bayram Sahin was born in Malatya, Turkey. He received his Bachelor's degree from Ege University, Izmir, Turkey, in 1993 and his Ph.D from Inonu University in 2000. After graduating, Dr. Sahin worked as a post-doctoral fellow at University of Windsor from March 2003 to September 2003 and a research scholar from June 2007 to September 2007. He has led several TUBITAK funded projects at the interface of manifold theory and maps and he has written (or co-authored) eighty-one academic papers. He is the author of the monograph "Differential Geometry of Lightlike Submanifolds (2010) and the editors of Turkish Journal of Mathematics and Mediterranean Journal of Mathematics. He is the recipient of Masatoshi Gunduz Ikeda research award at 2006. He is now a professor of Mathematics at Ege University, Turkey.

Contenu

1. Basic Geometric Structures on Manifolds 2. Applications of Riemannian Submersions 3. Riemannian submersions From Almost Hermitian Manifolds 4. Riemannian Maps 5. Riemannian Maps From Almost Hermitian Manifolds 6. Riemannian Maps To Almost Hermitian Manifolds