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:
“It is a secret from nobody that the famous random event is most likely to arise from those parts of the world where the old adage “There is no alternative to victory” retains a high degree of plausibility.”
—Hannah Arendt (1906–1975)
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)