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Approximation of Smooth Maps by Real Algebraic Morphisms

Published online by Cambridge University Press:  20 November 2018

Wojciech Kucharz  and
Kamil Rusek
Wojciech Kucharz
Affiliation:
University of New Mexico, Department of Mathematics and Statistics, Albuquerque, New Mexico 87131-1141, U.S.A., e-mail: kucharz@math.unm.edu
Kamil Rusek
Affiliation:
Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland, e-mail: rusek@im.uj.edu.pl
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Abstract

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Let 𝔾p,q(𝔽) be the Grassmann space of all q-dimensional 𝔽-vector subspaces of 𝔽p, where 𝔽 stands for ℝ, ℂ or ℍ (the quaternions). Here 𝔾p,q(𝔽) is regarded as a real algebraic variety. The paper investigates which C∞ maps from a nonsingular real algebraic variety X into 𝔾p,q(𝔽) can be approximated, in the C∞ compact-open topology, by real algebraic morphisms.

Keywords

14P0514P25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 456 - 463
Copyright
Copyright © Canadian Mathematical Society 1997

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