Old and New Euclidean Geometry and Analysis

Marcel Berger ()
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Marcel Berger: Institut des Hautes Études Scientifiques IHES

Chapter 1 in A Panoramic View of Riemannian Geometry, 2003, pp 1-99 from Springer

Abstract: Abstract Some (not all) of the following generalizes to any dimension; this will be left to the reader. We will only give references for special topics. General references could be Berger and Gostiaux 1988 [175], Coxeter 1989 [409], do Carmo 1976 [451], Klingenberg 1995 [816], Spivak 1979 [1155], Sternberg 1983 [1157], and Stoker 1989 [1160]. For those who like computer programming, Gray 1998 [584] will be of interest. We will assume elementary calculus and also that functions are differentiable as often as needed.

Keywords: Short Path; Riemannian Manifold; Fundamental Form; Principal Curvature; Euclidean Geometry (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-3-642-18245-7_1

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