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
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