Alternative Definitions
It is also given by
where is the covariant derivative and g is the metric tensor.
At a point p on a regular surface in R3, the Gaussian curvature is also given by
where S is the shape operator.
A useful formula for the Gaussian curvature is Liouville's equation in terms of the Laplacian in isothermal coordinates.
Read more about this topic: Gaussian Curvature
Famous quotes containing the words alternative and/or definitions:
“If you have abandoned one faith, do not abandon all faith. There is always an alternative to the faith we lose. Or is it the same faith under another mask?”
—Graham Greene (1904–1991)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)