Ideas of projective geometry keep reappearing in seemingly
unrelated fields of mathematics. The authors' main goal in this
2005 book is to emphasize connections between classical projective
differential geometry and contemporary mathematics and mathematical
physics. They also give results and proofs of classic theorems.
Exercises play a prominent role: historical and cultural comments
set the basic notions in a broader context. The book opens by
discussing the Schwarzian derivative and its connection to the
Virasoro algebra. One-dimensional projective differential geometry
features strongly. Related topics include differential operators,
the cohomology of the group of diffeomorphisms of the circle, and
the classical four-vertex theorem. The classical theory of
projective hypersurfaces is surveyed and related to some very
recent results and conjectures. A final chapter considers various
versions of multi-dimensional Schwarzian derivative. In sum, here
is a rapid route for graduate students and researchers to the
frontiers of current research in this evergreen subject.
Cambridge University Press (Virtual Publishing)
|Country of origin:
||Cambridge Tracts in Mathematics, 165
• Serge Tabachnikov
||Electronic book text
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