eBook ISBN:  9781470402082 
Product Code:  MEMO/130/619.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $30.00 
eBook ISBN:  9781470402082 
Product Code:  MEMO/130/619.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $30.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 130; 1997; 143 ppMSC: Primary 53; 58; Secondary 70
Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and KählerLiouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
ReadershipGraduate students and research mathematicians interested in differential geometry and hamiltonian mechanics.

Table of Contents

Chapters

Part 1. Liouville manifolds

Introduction

1. Local structure of proper Liouville manifolds

2. Global structure of proper Liouville manifolds

3. Proper Liouville manifolds of rank one

Appendix. Simply connected manifolds of constant curvature

Part 2. KählerLiouville manifolds

Introduction

1. Local calculus on $M^1$

2. Summing up the local data

3. Structure of $MM^1$

4. Torus action and the invariant hypersurfaces

5. Properties as a toric variety

6. Bundle structure associated with a subset of $\mathcal {A}$

7. The case where $\#\mathcal {A}=1$

8. Existence theorem


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Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and KählerLiouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
Graduate students and research mathematicians interested in differential geometry and hamiltonian mechanics.

Chapters

Part 1. Liouville manifolds

Introduction

1. Local structure of proper Liouville manifolds

2. Global structure of proper Liouville manifolds

3. Proper Liouville manifolds of rank one

Appendix. Simply connected manifolds of constant curvature

Part 2. KählerLiouville manifolds

Introduction

1. Local calculus on $M^1$

2. Summing up the local data

3. Structure of $MM^1$

4. Torus action and the invariant hypersurfaces

5. Properties as a toric variety

6. Bundle structure associated with a subset of $\mathcal {A}$

7. The case where $\#\mathcal {A}=1$

8. Existence theorem