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ALMOST COMPLEX HOMOGENEOUS SPACES AND THEIR SUBMANIFOLDS
by K Yang (Arkansas State)
This book is an introduction to the theory of almost complex homogeneous spaces and certain closely related class of spaces, so called partial G-flag manifolds. Submanifolds, in particular holomorphic curves, are also treated using the theory of moving frames and the structure theory of compact lie groups. The exposition is reasonably self-contained and this book is strongly recommended as a text for beginning graduate students.
Contents:
- Structures of Compact Lie Groups: Definitions
and Examples
- Lie Algebras — Basic Results
- Orthogonal and Unitary Representations
- Maximal Tori and Stiefel Diagrams
- Weyl Groups, Dynkin Diagrams and the Classification
- Almost Complex Homogeneous Spaces: Homogeneous Spaces
- Partial G-Flag Manifolds and Invariant Metrics
- Invariant Complex Structures
- The Maurer-Cartan Form
- Integrability Condition
- The Horizontal Distribution
- Complex Submanifolds: Pseudocomplex Maps
- Moving Frames
- U(n)-Flag Manifolds
- SO(2n,R)-Flag Manifolds
- Examples: Holomorphic Curves: Holomorphic Curves in F1,2,3(C3)
- Horizontal Curves U(n)/T
- Holomorphic Curves in CPm
- Horizontal Curves in Sp(n)/T
- Algebraic Curves: Singular Metrics and the Gauss-Bonnet-Chem Theorem
- Project Curves and Their Associated Curves
- Horizontal Curves and the Frenet Frames
- Plücker Formulae for Projective Curves
- The Symplectic Plücker Formulae
- Exterior Differential Systems: Exterior Algebra, Completely Integrable Systems and the Cauchy Characteristics
- Cartan-Kähler Theory
- Prolongation
Readership: Mathematicians and theoretical physicists.
| 124pp |
Pub. date: Dec 1987 |
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