Projective Metric definition of Projective Metric in the Free Online Encyclopedia.

Projective Metric

a method of measuring lengths and angles by means of projective geometry. In a projective metric, some figure is taken as an absolute determining the given metric geometry, and the transformations that map the absolute into itself and thus generate a corresponding group of motions are singled out from the group of all projective transformations. For example, the metric of the Lobachevskian plane is obtained if a nondegenerate real quadratic curve is taken as the absolute. The length of the line segment A B is then equal to λ In (ABPQ), where P and Q are the points at which the line A B intersects the absolute, (ABPQ) is the cross ratio, and λ is a constant identical for all segments. If a quadratic curve without real points is used to measure lengths and angles, elliptic geometry is obtained. Degenerate quadratic curves are used to construct Euclidean and Minkowskian geometry.

Mentioned in	?		Encyclopedia browser	?		Full browser	?
No references found			projection area projection booth projection cathode-ray tube projection chamber projection display projection fibers projection microradiography projection microscope projection net Projection Operator projection optics projection plan position indicator projection printer projection printing projection slide projection spark chamber Projection Television projection thermography projection TV projection welding projection, map projectionist Projective Geometry projective group projective line Projective Metric projective plain curve Projective Plane projective point Projective Space projective technique projective test projective topology Projective Transformation Projector projector compass Projector, Light projet Prokaryotae Prokaryote Prokey Prokhladnyi Prokhor of Gorodets Prokhorov Prokhorov, Aleksandr Prokhorov, Aleksandr Mikhailovich Prokhorov, Aleksei Prokhorov, Aleksei Nikolaevich Prokhorov, Iurii Prokhorov, Iurii Vasilevich Prokhorovka			projectionists projectionists projectionists Projections Projections Projections Projections Projections Projections of Broken Capsular Matrix Projections onto Convex Set projective projective projective projective projective Projective algebraic variety Projective curve projective device Projective General Linear projective geometry projective geometry projective geometry Projective Geometry Low-Density Parity-Check Projective group Projective identification Projective infinity Projective line Projective linear group Projective map Projective method Projective Metric Projective orthogonal group Projective personality assessment Projective personality test Projective personality test Projective personality test projective plain curve Projective plane projective point Projective psychological test Projective space Projective space over a division algebra Projective Special Linear Projective special orthogonal group Projective special unitary group Projective surface projective technique projective technique projective technique Projective techniques Projective techniques Projective techniques projective test projective test projective test projective test projective test Projective tests Projective tests Projective tests Projective topology

Projective Metric

REFERENCES