Parallel frame of non-lightlike curves in
Minkowski space-time. International Journal of Geometric Methods in Modern Physics, 12(10), 1550109.
From the geometrical point of view, the metric in (9) describes a
Minkowski space-time with a conical singularity [23].
in the
Minkowski space-time over real axis x [member of] R.
A., Conformal
Minkowski space-time. I - Relative infinity and proper time, Il Nuovo Cimento B, 72, 261-272, (1982).
It details the theory of contact and its connection to the theory of caustics and wavefronts, then applies these theories to deduce geometric information about surfaces embedded in three, four, and five-dimensional Euclidean spaces, as well as spacelike surfaces in the
Minkowski space-time. It discusses the basic facts about the extrinsic geometry of submanifolds of Euclidean spaces, singularities of smooth mappings, the theory of contact introduced by Mather and developed by Montaldi, basic concepts in symplectic and contact geometry and the connection to the theory of contact and Lagrangian and Legendrian singularities, and global results on closed surfaces using local invariants obtained from the the local study of surfaces.
At the beginning of the twentieth century Einstein's theory opened a door to new geometries such as
Minkowski space-time, which is simultaneously the geometry of special relativity and the geometry induced on each fixed tangent space of an arbitrary Lorentzian manifold.
Recently, a new special curve is named according to the Sabban frame in the Euclidean unit sphere; Smarandache curve has been defined by Turgut and Yilmaz in
Minkowski space-time [1].
Zampetti, Geometry of
Minkowski Space-Time, Birkhauser, Boston, Mass, USA, 2011.
Rectifying curves in the
Minkowski space-time [E.sup.4.sub.1] are defined and studied in [4].
Galilean spacetime plays the same role in nonrelativistic physics that
Minkowski space-time does in relativistic physics.
Bonnor [7] in
Minkowski space-time. In the same space, Frenet equations for some special null; Partially and Pseudo Null curves are given in [4].