Differential Geometry

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By Michael Spivak

ISBN-10: 0914098713

ISBN-13: 9780914098713

Publication via Michael Spivak, Spivak, Michael

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Extra info for A Comprehensive Introduction to Differential Geometry Volume 2, Third Edition

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Clearly it is equal to the Grassmannian of (l + 1)-dimensional complex linear subspaces in Cn+1 . 4) l where dE is the Haar measure on C G normalized in some way (we do not care about normalization constants). 5) where c = 0 is a normalizing constant depending on normalizations of Haar measures and l, m, n. Let us give a heuristic proof of this equality. 8, we observe that φl (K) = 1lE dE (K), CG l where 1lE is considered as a generalized valuation. 14. Since for generic projective subspaces E and F their intersection E ∩ F is a projective subspace of dimension l + m − n for l + m ≥ n and empty otherwise, it follows that CG l× 1lM dM = c · φl+m−n .

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Of Math. 173 (2011), 907–945. : On the curvatura integra in a Riemannian manifold. Ann. of Math. 46 (1945), 674–684. : Curvature measures. Trans. Amer. Math. Soc. 93 (1959), 418– 491. [28] Fu, J. H. : Curvature measures and generalized Morse theory, J. Differential Geom. 30 (1989), 619–642. [29] Fu, J. H. : Monge–Amp`ere functions, I. Indiana Univ. Math. J. 38 (1989), no. 3, 745–771. Bibliography 43 [30] Fu, J. H. : Monge–Amp`ere functions, II. Indiana Univ. Math. J. 38 (1989), no. 3, 773–789. [31] Fu, J.

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A Comprehensive Introduction to Differential Geometry Volume 2, Third Edition by Michael Spivak

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