Generalisation of Clairaut's theorem to Minkowski spaces

TL;DRAbstract

The geometry of surfaces of rotation in three dimensional Euclidean space has been studied widely. The rotational surfaces in three dimensional Euclidean space are generated by rotating an arbitrary curve about an arbitrary axis. \n Moreover, the geodesics on surfaces of rotation in three dimension Euclidean space have been considered and discovered. Clairaut's [1713-1765] theorem describes the geodesics on surfaces of rotation and provides a result which is very helpful in understanding all geodesics on these surfaces. \n On the other hand, the Minkowski spaces have shorter history. In 1908 Minkowski [1864-1909] gave his talk on four dimensional real vector space, with asymmetric form of signature (+,+,+,-). In this space there are different types of vectors/axes (space-like- time-like and null) as well as different types of curves (space-like- time-like and null). This thesis considers the different types of axes of rotations, then creates three different types of surfaces of rotatio

Chat with Paper

AI Agents for this Paper