Space sections relative to a noninertial frame in Minkowski space-time

We define new coordinates using the family of accelerated Rindler observers in Minkowski space-time and study the spatial sections (hypersurfaces of simultaneity) adapted to the noninertial frame that arises from our definition. We show that the geometry of the spatial sections is not Euclidean. Owing to this feature, the new noninertial frame can be employed to illustrate, in a simple way, the connection between acceleration and non-Euclidean geometry in the relativistic context.