Vipul: 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 $a,c$ . I..."

2011-08-12T12:58:59Z

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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==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>. 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.

Circular hyperboloid of one sheet - Revision history

Vipul: 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 a,c. I..."

Vipul: 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 $a,c$ . I..."