About A Slater Euclidean Metric

Let us consider here, what is to be happening -- if the following two things were to be happening, as two certain given arbitrary orbifold eigensets, -- are to be going through their respective unitary mean Lagrangian paths, over time:

1)  Let us say one were to have a tangential flow, via the course of an "identity function."

2) Let us also say that one were to have a co-tangential flow, via the course of an "identity function."

Consequently:

One would thus have two different situations, to where each one is here to exhibit the following common characteristic:  Both would bear a discrete & a topologically smooth Slater euclidean metric, that is here to be homeomorphic -- but Not flat.

Let's next say, that (the secant of (e^(the Cevita-based Flow))) = 2^.5, and;
                               (the co-secant of (e^(the Wess-Zumino-based Flow))) = 2^.5. 

As a result: ((((Integral Of (e^(the del of the Cevita-based Flow))))
                         = (((the inverse secant of e^((the Cevita-based Flow))) = 45 degrees.; and;
                   (((((Integral Of (e^(the del of the Wess-Zumino-based Flow)) ))
                         = (((the inverse co-secant of e^((the Wess-Zumino-based Flow))) = 45 degrees.

This would then work to make the reciprocal of the Inverse of both of the immediately prior, to be equal to (1/(2^.5)).
This eludes to the condition -- that the tense of either of such a flow as coming towards "you," would bear a tense of the cosine of 45 degrees (dot-product), or, of (1/2^.5);
And, this eludes, as well, to the condition -- that the tense of either of such a flow as going away from "you," would bear a tense of the sine of 45 degrees (cross-product), or, of (1/2^.5).
To Be Continued!  Sam Roach.