A systematic and self-contained treatment, this revised edition examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. Four appendixes deal with holomorphic bisectional curvature, Gauss-Bonnet theorem and its applications, and Bochner's Lemma.

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