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The tangent cone serves as the extension of the notion of the tangent space to X at a regular point, where X most closely resembles a differentiable manifold, to all of X. (The tangent cone at a point of that is not contained in X is empty.) For example, the nodal curve. is singular at the origin, because both partial derivatives of f ( x, y ...
Carolyn Kaster. Louisiana Gov. Jeff Landry has a suggestion for parents who don't believe the Ten Commandments should be displayed in public school classrooms throughout the state. "Tell your ...
The cone may have multiple branches, each one an affine cone over a simple closed curve in the projective tangent space. As the base point ,, varies, the cone also varies. Thus the Monge cone is a cone field on R 3. Finding solutions of (1) can thus be interpreted as finding a surface which is everywhere tangent to the Monge cone at the point.
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