A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd Edition by Michael Spivak (PDF)

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This book is the second volume of the 3rd edition in a five volume series on differential geometry. The focus here is on the foundations of curvature and connections. The only prerequisite for volume II is a careful study of volume I. In particular, you’ll need a good understanding of the Riemannian metric and you’ll need to be comfortable with manipulating differential forms. Also pay attention to the differential equations material used to establish Frobenius Integrability in Chapter 6 of volume I. In addition, you’ll need the main concepts from the Lie Groups study of Chapter 10 of volume I.

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