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

  • 1st Edition - January 23, 2017
  • Latest edition
  • Author: Bayram Sahin
  • Language: English

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersio… Read more

Description

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.

Key features

  • 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

Readership

Graduate students and researchers who have good knowledge of Riemannian geometry and its submanifolds and interest in the Riemannian submersions and Riemannian maps, extending to applied mathematicians, mathematical physicists, mathematical statistics, mechanical engineers and mechatronic engineers

Table of contents

  • Dedication
  • Acknowledgments
  • Preface
  • About the Author
  • Chapter 1: Basic Geometric Structures on Manifolds
    • Abstract
    • 1 Riemannian manifolds and related topics
    • 2 Vector bundles
    • 3 Riemannian submanifolds and distributions
    • 4 Riemannian submersions
    • 5 Certain product structures on manifolds
    • 6 Geometric structures along a map
  • Chapter 2: Applications of Riemannian Submersions
    • Abstract
    • 1 Applications of Riemannian submersions in robotic theory
    • 2 Kaluza-Klein theory
  • Chapter 3: Riemannian submersions From Almost Hermitian Manifolds
    • Abstract
    • 1 Almost Hermitian manifolds
    • 2 Holomorphic submersions and invariant submersions
    • 3 Anti-invariant Riemannian submersions
    • 4 Semi-invariant submersions
    • 5 Generic Riemannian submersions
    • 6 Slant submersions
    • 7 Semi-slant submersions
    • 8 Hemi-slant submersions
    • 9 Pointwise slant submersions
    • 10 Einstein metrics on the total space of an anti-invariant submersion
    • 11 Clairaut submersions from almost Hermitian manifolds
  • Chapter 4: Riemannian Maps
    • Abstract
    • 1 Riemannian maps
    • 2 Geometric structures along Riemannian maps
    • 3 Totally geodesic Riemannian maps
    • 4 Umbilical Riemannian maps
    • 5 Harmonicity of Riemannian maps
    • 6 Clairaut Riemannian maps
    • 7 Circles along Riemannian maps
    • 8 Chen first inequality for Riemannian maps
    • 9 Einstein metrics on the total space of a Riemannian map
  • Chapter 5: Riemannian Maps From Almost Hermitian Manifolds
    • Abstract
    • 1 Holomorphic Riemannian maps from almost Hermitian manifolds
    • 2 Anti-invariant Riemannian maps from almost Hermitian manifolds
    • 3 Semi-invariant Riemannian maps from almost Hermitian manifolds
    • 4 Generic Riemannian maps from almost Hermitian manifolds
    • 5 Slant Riemannian maps from almost Hermitian manifolds
    • 6 Semi-slant Riemannian maps from almost Hermitian manifolds
    • 7 Hemi-slant Riemannian maps from almost Hermitian manifolds
  • Chapter 6: Riemannian Maps To Almost Hermitian Manifolds
    • Abstract
    • 1 Invariant Riemannian maps to almost Hermitian manifolds
    • 2 Anti-invariant Riemannian maps to almost Hermitian manifolds
    • 3 Semi-invariant Riemannian maps to almost Hermitian manifolds
    • 4 Generic Riemannian maps to Kähler manifolds
    • 5 Slant Riemannian maps to Kähler manifolds
    • 6 Semi-slant Riemannian maps to Kähler manifolds
    • 7 Hemi-slant Riemannian maps to Kähler manifolds
  • Bibliography
  • Index

Review quotes

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

Product details

  • Edition: 1
  • Latest edition
  • Published: January 23, 2017
  • Language: English

About the author

BS

Bayram Sahin

Bayram Şahin was born in Malatya, Turkey. He received his Bachelor’s degree from Ege University, İzmir, Turkey, in 1993 and his Ph.D from Inonu University in 2000. After graduating, Dr. Şahin 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.
Affiliations and expertise
Ege University, Turkey

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