nLab Klein quadric



A projective variety that is moreover a quadric given by zeroes of the quadratic form

x 0x 5+x 1x 4+x 2x 3 x_0x_5 + x_1 x_4 + x_2 x_3

where [x 0:x 1:x 2:x 3:x 4:x 5][x_0:x_1:x_2:x_3:x_4:x_5] are homogeneous coordinates on 5\mathbb{P}^5. It was studied in (Klein 1868), together with what is now called the Klein correspondence?, by Felix Klein in his 1868 dissertation under Julius Plücker?.


The conformal compactification, of complexified Minkowski spacetime 3,1\mathbb{R}^{3,1}, is given by the Klein quadric. (eg, Fioresi-Lledo-Varadarajan 07, section 2).


Last revised on July 29, 2016 at 07:55:14. See the history of this page for a list of all contributions to it.