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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

Homogeneous spaces --- Submanifolds --- 514.763.4 --- 514.763.4 Manifolds with complex or almost-complex structure. Hermitian manifolds. Kähler manifolds --- Manifolds with complex or almost-complex structure. Hermitian manifolds. Kähler manifolds --- Geometry, Differential --- Manifolds (Mathematics) --- Spaces, Homogeneous --- Lie groups --- Submanifolds. --- Homogeneous spaces.