Circles and Quadratic Maps Between Spheres |
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Authors: | Email author" target="_blank">Vladlen?TimorinEmail author |
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Institution: | (1) Institute for Mathematical Sciences, SUNY at Stony Brook, NY, 11794-3660, U.S.A |
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Abstract: | Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs
of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation
on roundings and prove that any rounding, whose differential at 0 has rank at least 2, is equivalent to a fractional quadratic
rounding. A fractional quadratic map is just the ratio of a quadratic map and a quadratic polynomial. We also show that any
rounding gives rise to a quadratic map between spheres. The known results on quadratic maps between spheres have some interesting
implications concerning roundings.
Partially supported by CRDF RM1-2086. |
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Keywords: | line circle quadratic map between spheres normed pairing |
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