A 4D space with the Minkowski Metric. Alternatively, it can be considered to have a Euclidean Metric, but
with its Vectors defined by

(1) 
where is the speed of light. The Metric is Diagonal with

(2) 
so

(3) 
Let be the Tensor for a Lorentz Transformation. Then

(4) 

(5) 

(6) 
The Necessary and Sufficient conditions for a metric to be equivalent to the Minkowski metric
are that the Riemann Tensor vanishes everywhere (
) and that at
some point has three Positive and one Negative Eigenvalues.
See also Lorentz Transformation, Minkowski Metric
References
Thompson, A. C. Minkowski Geometry. New York: Cambridge University Press, 1996.
© 19969 Eric W. Weisstein
19990526