Almost complex homogeneous spaces and their submanifolds / Kichoon Yang.

Format:

Book

Author/Creator:

Yang, Kichoon, author.

Language:

English

Subjects (All):

Submanifolds.

Homogeneous spaces.

Physical Description:

1 online resource (123 p.)

Place of Publication:

Singapore : World Scientific, 1987.

Language Note:

English

Summary:

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 Di

Contents:

Preface; TABLE OF CONTENTS; Chapter I STRUCTURES OF COMPACT LIE GROUPS; 1. Definitions and Examples; 2 Lie Algebra: Basic Results; 3. Orthogonal and Unitary Representations; 4. Maximal Tori and Stiefel Diagrams; 5. Weyl Groups; 6. Dynkin Diagrams and the Classification; Chapter II ALMOST COMPLEX HOMOGENEOUS SPACES; 7. Homogeneous Spaces; 8. Partial G-Flag Manifolds and Invariant Metrics; 9. Invariant Complex Structures; 10. The Maurer-Cartan Form; 11. Integrability Condition; 12. The Horizontal Distribution; Chapter III COMPLEX SUBMANIFOLDS; 13. Pseudocomplex Maps

14. Moving Frames15. U(n)-flag Manifold; 16. SO(2n; R)-flag Manifolds; Chapter IV EXAMPLES: HOLOMORPHIC CURVES; 17. Holomorphic Curves in F1,2,3(C^3); 18. Horizontal Curves in U(n)/T; 19. Holomorphic Curves in CP^m; 20. Horizontal Curves in Sp(n)/T; Chapter V ALGEBRAIC CURVES; 21. Singular Metrics and the Gauss-Bonnet-Chern Theorem; 22. Protective Curves and Their Associated Curves; 23. Horizontal Curves and the Frenet Frames; 24. Plυc̈ker Formulae for Projective Curves; 25. The Symplectic Plυc̈ker Formulae; Appendix EXTERIOR DIFFERENTIAL SYSTEMS; 1. Exterior Algebra

2. Completely Integrable Systems and the Cauchy Characteristics3. Cartan-Kähler Theory; 4. Prolongation; REFERENCES; INDEX

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9789814503235

9814503231