Learn More
We study the neutral Kähler metric on the space of time-like lines in Lorentzian E 3 1 , which we identify with the total space of the tangent bundle to the hyperbolic plane. We find all of the infinitesimal isometries of this metric, as well as the geodesics, and interpret them in terms of the Lorentzian metric on E 3 1. In addition, we give a new(More)
We study surfaces in TN that are area-stationary with respect to a neutral Kähler metric constructed on TN from a riemannian metric g on N. We show that holomorphic curves in TN are area-stationary, while lagrangian surfaces that are area-stationary are also holomorphic and hence totally null. However, in general, area stationary surfaces are not(More)
The space L of oriented lines, or rays, in R 3 is a 4-dimensional space with an abundance of natural geometric structure. In particular, it boasts a neutral Kähler metric which is closely related to the Euclidean metric on R 3. In this paper we explore the relationship between the focal set of a line congruence (or 2-parameter family of oriented lines in R(More)