The Infinite Regions of Various Geometries
Author: Maxime Bocher
Publisher:
Published: 1914
Total Pages: 72
ISBN-13:
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Author: Maxime Bocher
Publisher:
Published: 1914
Total Pages: 72
ISBN-13:
DOWNLOAD EBOOKAuthor: Julian Lowell Coolidge
Publisher:
Published: 1924
Total Pages: 252
ISBN-13:
DOWNLOAD EBOOKAuthor: David E. Blair
Publisher: American Mathematical Soc.
Published: 2000-08-17
Total Pages: 130
ISBN-13: 0821826360
DOWNLOAD EBOOKIt is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or independent study. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites.
Author: Oswald Veblen
Publisher:
Published: 1918
Total Pages: 536
ISBN-13:
DOWNLOAD EBOOKAuthor: American Mathematical Society
Publisher:
Published: 1915
Total Pages: 660
ISBN-13:
DOWNLOAD EBOOKAuthor: Tsuruichi Hayashi
Publisher:
Published: 1914
Total Pages: 234
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 1914
Total Pages: 592
ISBN-13:
DOWNLOAD EBOOKAuthor: Julian Lowell Coolidge
Publisher:
Published: 1916
Total Pages: 603
ISBN-13:
DOWNLOAD EBOOKAuthor: Boris Khesin
Publisher: Springer Science & Business Media
Published: 2008-09-28
Total Pages: 304
ISBN-13: 3540772634
DOWNLOAD EBOOKThis monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.