MTU Library Catalogue

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Riemannian geometry : a beginner's guide / Frank Morgan, illustrated by James F. Bredt.

By: Morgan, Frank.
Material type: materialTypeLabelBookSeries: Jones and Bartlett books in mathematics.Publisher: Boston : Jones and Bartlett Publishers, c1993Description: 119 p. : ill. ; 24 cm. + hbk.ISBN: 0867202424.Subject(s): Geometry, RiemannianDDC classification: 516.373
Contents:
Introduction -- Curves in Rn -- Surfaces in R3 -- Surfaces in Rn -- m-dimensional surfaces in Rn -- Intrinsic Riemannian geometry -- General relativity -- The Gauss-bonnet theorem -- Geodesics and global geometry -- General norms.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 516.373 (Browse shelf(Opens below)) 1 Available 00014610
Total holds: 0

Enhanced descriptions from Syndetics:

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Bibliography: (pages 105-108) and indexes.

Introduction -- Curves in Rn -- Surfaces in R3 -- Surfaces in Rn -- m-dimensional surfaces in Rn -- Intrinsic Riemannian geometry -- General relativity -- The Gauss-bonnet theorem -- Geodesics and global geometry -- General norms.

Reviews provided by Syndetics

CHOICE Review

Differential geometry is a forbidding subject for the neophyte, with geometric insights difficult to decipher amidst the mountains of technical formulas. Morgan uses the study of curvature as a unifying and demystifying theme for his introduction to differential geometry. With simple elegance he takes the reader through a concrete tour of parameterized curves in space, surfaces in 3-space and n-space, and general m-dimensional surfaces in Euclidean n-space, wisely using extrinsic coordinates to develop intrinsic Riemannian geometry. The result is an astoundingly brief and uncluttered text, but one which demands considerable notational sophistication from the reader and excellent command of prerequisite topics such as (second-year undergraduate level) vector calculus and linear algebra. Standard topics such as Gauss's Theorema Egregium (on p. 20!), Riemannian metrics and tensors, hyperbolic geometry, and the Gauss-Bonnet Theorem are treated, as are special subjects such as an introduction to general relativity and recent research on norm-minimizing networks by the author and Williams College undergraduates. Highly recommended for the ambitious reader. S. J. Colley; Oberlin College