In Riemannian geometry all lines perpendicular to a given li

In Riemannian geometry all lines perpendicular to a given line are not concurrent. true or false

Solution

We know that the meridians of a globe pass through the north pole and are perpendicular to the equator. From this simple observation we can deduce some facts about the Riemann plane.

There exists a unique line perpendicular to all the lines of a given pencil, every pencil is a hyperpencil. Conversely, since the perpendiculars to a given line are concurrent, every hyperpencil is a pencil.

Therefore, the statement \"In Riemannian geometry all lines perpendicular to a given line are not concurrent\". is false.