Then the Codazzi-Mainardi equation expressing a compatibility condition between the first and second fundamental forms results in the sine-Gordon equation.
22.
Here the curvature of a curve is by definition the principal axes of a symmetric tensor & mdash; the second fundamental form.
23.
We assume that " M " has no points where the second fundamental form is transverse vector field over " M ".
24.
While the exterior style may vary the fundamental form and principles of Vaastu Shastras were used as far back as King Solomon's temple.
25.
Stockhausen used a basic graphic notation to indicate how each loop should be altered from its fundamental form through pitch and tempo changes.
26.
Stein has had a powerful effect, too, on writers like Donald Barthelme and William Gass who have questioned the fundamental forms of fiction.
27.
To connect this point of view with the embedded into "'R "'3 and endowed with the Riemannian metric given by the first fundamental form.
28.
The first fundamental form evaluated on this pair of vectors is their dot product, and the angle can be found from the standard formula
29.
The second fundamental form, which determines the full curvature via the principal directions of the hypersurface are also the eigendirections of the Ricci tensor.
30.
The first equation is the "'Gauss equation "'which expresses the curvature form ? of " M " in terms of the second fundamental form.
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