Gaussian Curvature - Alternative Definitions

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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