Real Algebraic and Analytic Geometry
Submission: 2002, April 25.
We determine all complete intersection surface germs whose Pythagoras number is 2, and find they are all embedded in R^3 and have the property that every positive semidefinite analytic function germ is a sum of squares of analytic function germs. In addition, we discuss completely these properties for mixed surface germs in R^3. Finally, we find in higher embedding dimension three different families with these same properties.
Mathematics Subject Classification (2000): 11E25, 14P15.
Keywords and Phrases: Pythagoras number, mixed and unmixed surface germs, sums of squares.
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