Variation of shape operator under infinitesimal bending of surface

摘要

In case of bendable surfaces it is useful to discuss the variation of magnitudes such as the shape operator. The shape operator is a good way to measure how a regular surface S bends in R3 by valuation how the surface normal ν changes from point to point. We considered the variation of shape operator under infinitesimal bending of surface given in an explicit form. We also gave two examples of the variation of shape operator of Gaudi surface and hyperbolic paraboloid.