Complex Minkowski spacetime
In his second relativity paper in 1905–06 Henri Poincaré showed how, by taking time to be an imaginary fourth spacetime coordinate ict, where c is the speed of light and i is the

It is assumed below that spacetime is endowed with a coordinate system corresponding to an inertial frame. This provides an origin, which is necessary in order to be able to refer to spacetime as being modeled as a vector space. This is not really physically

The meaning of the term geometry for the Minkowski space depends heavily on the context. Minkowski space is not endowed with a Euclidean geometry, and not with any of the generalized Riemannian geometries with intrinsic curvature, those exposed by the model

Where v is velocity, and x, y, and z are Cartesian coordinates in 3-dimensional space, and c is the constant representing the universal speed limit, and t is time, the four-dimensional vector v = (ct, x, y, z) = (ct, r) is classified according to the sign of c t − r . A vector is timelike

Time-like vectors have special importance in the theory of relativity as they correspond to events which are accessible to the observer at (0, 0, 0,

A Lorentzian manifold is a generalization of Minkowski space in two ways. The total number of spacetime dimensions is not restricted to be 4 (2 or more) and a Lorentzian manifold need not be flat, i.e. it allows for curvature.
Complexified Minkowski

• Hyperspace
• Introduction to the mathematics of general relativity
• Minkowski plane