Shape Operator
The negative derivative
 | (1) |
vector field of a Surface is called the shape operator (or Weingarten Map orSecond Fundamental Tensor). The shape operator 
is an Extrinsic Curvature, and the Gaussian Curvatureis given by the Determinant of . If 
is a Regular Patch, then |  |  | (2) |
 | |  | (3) |
At each point p on a Regular Surface
, the shape operator is a linear map | (4) |
References
Gray, A. ``The Shape Operator,'' ``Calculation of the Shape Operator,'' and ``The Eigenvalues of the Shape Operator.'' §14.1, 14.3, and 14.4 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 268-269, 274-279, 1993. Reckziegel, H. In Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, p. 30, 1986.
- Dirichlet Fourier Series Conditions
- Dirichlet Function
- Dirichlet Integrals
- Dirichlet Kernel
- Dirichlet Lambda Function
- Dirichlet L-Series
- Dirichlet Region
- Dirichlet's Boxing-In Principle
- Dirichlet's Box Principle
- Dirichlet Series
- Dirichlet's Formula
- Dirichlet's Lemma
- Dirichlet's Principle
- Dirichlet's Test
- Dirichlet's Theorem
- Dirichlet Structure Constant
- Dirichlet Tessellation
- Dirty Beam
- Dirty Map
- Disc
- Disconnected Form
- Disconnectivity
- Discontinuity
- Discontinuous
- Discordant Permutation