Gauss Map - Total Curvature

The area of the image of the Gauss map is called the total curvature and is equivalent to the surface integral of the Gaussian curvature. This is the original interpretation given by Gauss. The Gauss-Bonnet theorem links total curvature of a surface to its topological properties.

Read more about this topic:  Gauss Map

Famous quotes containing the word total:

    I have often thought that if photography were difficult in the true sense of the term—meaning that the creation of a simple photograph would entail as much time and effort as the production of a good watercolor or etching—there would be a vast improvement in total output. The sheer ease with which we can produce a superficial image often leads to creative disaster.
    Ansel Adams (1902–1984)