CHAPTER III: CONICS AND QUADRICS - OCW UPM

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AFFINE <strong>AND</strong> PROJECTIVE GEOMETRY, E. Rosado & S.L. Rueda b) If sign(b 00 ) ≠ sign(λ 1 ), the reduced equation is of the form 0 = p 2 − a 2 x 2 1 = (p + ax 1 )(p − ax 1 ) and the affine quadric is a pair of parallel planes.
AFFINE <strong>AND</strong> PROJECTIVE GEOMETRY, E. Rosado & S.L. Rueda Table of classification of quadrics with det A 00 = 0 det A 00 = 0 ⎧ ⎪⎨ ⎪⎩ rank(A) = 4 Regular rank(A) = 3 Cylinders rank(A) = 2 Pair of planes rank(A) = 1 { J > 0 Elliptic paraboloid ⎧ ⎪⎨ J < 0 J > 0 J < 0 ⎪⎩ J = 0 ⎧ J > 0 ⎪⎨ J < 0 ⎪⎩ J = 0 double plane Hyperbolic paraboloid Real elliptic cylinder Hyperbolic cylinder Parabolic cylinder Pair of imaginary planes (line) Pair of secant planes Pair of parallel planes { imaginary real
Page 1 and 2: AFFINE AND PROJECTIVE GEOMETRY, E.
Page 9 and 10: 4.1.1 Projective classification AFF
Page 15 and 16: with discriminant AFFINE AND PROJEC
Page 17 and 18: 3. If P ∈ Q is a singular point,
Page 21 and 22: 4.4.3 Diameters of a quadric AFFINE
Page 27 and 28: 4.5 Metric invariants of a quadric
Page 29 and 30: 4.5.1 Classification of quadrics wi
Page 39: AFFINE AND PROJECTIVE GEOMETRY, E.

CHAPTER III: CONICS AND QUADRICS - OCW UPM

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