Difference between revisions of "Circular hyperboloid of one sheet"

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(Created page with "==Definition== The surface type is ''not'' unique up to isometry or even up to similarity transformations, but rather, depends on multiple nonzero parameters <math>a,c</math>. I...")
 
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Latest revision as of 12:58, 12 August 2011

Definition

The surface type is not unique up to isometry or even up to similarity transformations, but rather, depends on multiple nonzero parameters a,c. If we're considering the surface up to rigid isometries, the parameters are unique. If we're considering the surface up to similarity transformations, the parameters are unique up to projective equivalence.

Under affine transformations, a circular hyperboloid of one sheet need not remain a circular hyperboloid of one sheet. However, it is true that any two circular hyperboloids of one sheet are equivalent under affine transformations. So in this sense, the surface is unique up to affine transformations.