Miklos Schweitzer 1979_6
Source: pseudo-Riemannian metric
January 28, 2009
analytic geometryconicsadvanced fieldsadvanced fields unsolved
Problem Statement
Let us defined a pseudo-Riemannian metric on the set of points of the Euclidean space not lying on the -axis by the metric tensor \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & \minus{}\sqrt{x^2\plus{}y^2} \\ \end{array} \right), where is a Cartesian coordinate system . Show that the orthogonal projections of the geodesic curves of this Riemannian space onto the -plane are straight lines or conic sections with focus at the origin
P. Nagy