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Differential Geometry: Manifolds, Curves, and Surfaces - Manifolds, Curves, and Surfaces (Hardcover, 1988 ed.)
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Differential Geometry: Manifolds, Curves, and Surfaces - Manifolds, Curves, and Surfaces (Hardcover, 1988 ed.)
Series: Graduate Texts in Mathematics, 115
Expected to ship within 10 - 15 working days
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This book consists of two parts, different in form but similar in
spirit. The first, which comprises chapters 0 through 9, is a
revised and somewhat enlarged version of the 1972 book Geometrie
Differentielle. The second part, chapters 10 and 11, is an attempt
to remedy the notorious absence in the original book of any
treatment of surfaces in three-space, an omission all the more
unforgivable in that surfaces are some of the most common
geometrical objects, not only in mathematics but in many branches
of physics. Geometrie Differentielle was based on a course I taught
in Paris in 1969- 70 and again in 1970-71. In designing this course
I was decisively influ enced by a conversation with Serge Lang, and
I let myself be guided by three general ideas. First, to avoid
making the statement and proof of Stokes' formula the climax of the
course and running out of time before any of its applications could
be discussed. Second, to illustrate each new notion with
non-trivial examples, as soon as possible after its introduc tion.
And finally, to familiarize geometry-oriented students with
analysis and analysis-oriented students with geometry, at least in
what concerns manifolds."
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