Complex Manifolds

The following sections are included:

• Complex structure of manifolds, almost complex manifolds

• Integrable condition of almost complex structure

• Hermitian manifold

• Kähler manifold

• Connections on complex manifold

• Riemannian symmetric space, its Kähler structure and nonlinear realization

• Nonlinear σ-models, soliton solutions and their geometric meaning

• Notations and Formulae

• Exercises