Real Algebraic and Analytic Geometry |

On the Pythagoras numbers of real analytic set germs.

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homepages: http://www.uam.es/josefrancisco.fernando,
http://www.mat.ucm.es/~jesusr

Submission: 2003, April 14.

*Abstract:
We show that: (i) the Pythagoras number of a real analytic set germ is the supremum
of the Pythagoras numbers of the curve germs it contains, and (ii) every real
analytic curve germ is contained in a real analytic surface germ with the same Pythagoras
number (or Pythagoras number 2 if the curve is Pythagorean). This gives new
examples and counterexamples concerning sums of squares and positive semide.nite
analytic function germs.*

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