Klein's quadric

The Klein quadric is in projective geometry a conical quadric in 5-dimensional projective space , which is defined in homogeneous coordinates by the equation

${\displaystyle x_{0}x_{5}-x_{1}x_{4}+x_{2}x_{3}=0}$

is described.

It parameterizes straight lines in three-dimensional projective space, see Plücker coordinates .

literature

• Felix Klein : About the transformation of the general equation of the second degree between line coordinates to a canonical form . Dissertation (1868) published in Math. Ann 23 (1884), 539-578.

Web links

• Small quadric (nLab)
• The Klein quadric and triality