Transcription of INTRODUCTION TO DIFFERENTIAL GEOMETRY - ETH Z
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INTRODUCTION TO DIFFERENTIAL GEOMETRY - ETH Z
INTRODUCTION TODIFFERENTIAL GEOMETRYJoel W. RobbinUW MadisonDietmar A. SalamonETH Z urich19 December 2021iiPrefaceThese are notes for the lecture course DIFFERENTIAL GEOMETRY I given by thesecond author at ETH Z urich in the fall semester 2017. They are based ona lecture course1given by the first author at the University of Wisconsin Madison in the fall semester can distinguishextrinsic DIFFERENTIAL geometryandintrinsic differ-ential GEOMETRY . The former restricts attention to submanifolds of Euclideanspace while the latter studies manifolds equipped with a Riemannian extrinsic theory is more accessible because we can visualize curves andsurfaces inR3, but some topics can best be handled with the intrinsic definitions in Chapter 2 have been worded in such a way that it is easyto read them either extrinsically or intrinsically and the subsequent chaptersare mostly (but not entirely) extrinsic.
The third section builds on Chapter 5 on isometries and the Rie-mann curvature tensor. It contains a proof of the Myers{Steenrod Theorem, ... Lie algebra is nondegenerate, to establish uniqueness up to conjugation of maximal compact subgroups of the automorphism group of a semisimple Lie algebra, and to prove Cartan’s theorem about the ...
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