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

Author： Sahin Bayram

Publisher： Elsevier Science‎

Publication year： 2017

E-ISBN: 9780128044100

P-ISBN(Paperback): 9780128043912

Subject： O186.12 Riemannian geometry

Keyword：应用数学,数理科学和化学

Language： ENG

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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.

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

Chapter

Front Cover

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

CHAPTER 1: Basic Geometric Structures on Manifolds

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

1. Applications of Riemannian submersions in robotic theory

2. Kaluza-Klein theory

CHAPTER 3: Riemannian submersions From Almost Hermitian Manifolds

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

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

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

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

Bibilography

Index

Back Cover

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