否决
发表于 2025-3-25 05:34:28
Curves in Curves in the plane . are special in several respects: For a closed plane curve . an enclosed area . can be defined, providing another geometric functional in addition to length and bending energy.
尖叫
发表于 2025-3-25 10:51:46
Parallel Normal FieldsFor curves . there is an analog .of the curvature function of a plane curve. In the context of unit speed curves, this function . determines . up to an orientation-preserving rigid motion of .. Before we can define ., we have to study . along a curve in ..
GRILL
发表于 2025-3-25 13:37:15
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Kindle
发表于 2025-3-25 19:37:56
Surfaces and Riemannian GeometryThe most simple quantity of a one-dimensional curve . is its speed ..
Hectic
发表于 2025-3-25 20:39:51
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道学气
发表于 2025-3-26 00:32:55
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确保
发表于 2025-3-26 05:40:01
Levi-Civita ConnectionThe . of a surface . provides a geometrically meaningful way to take directional derivatives of a vector field . on .. Based on the Levi-Civita connection we derive two important equations that are satisfied by the curvature of a surface in .: the . and the ..
摆动
发表于 2025-3-26 08:49:27
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Calculus
发表于 2025-3-26 15:12:22
Closed SurfacesWe define a . as a surface . whose boundary components have been matched in pairs in such a way that . as well as its unit normal . are continuous across the boundary. This allows us to prove an analog of the fact that the tangent winding number of a closed plane curve is an integer.
去世
发表于 2025-3-26 20:14:16
Variations of SurfacesWe derive the basics of Vector Calculus on surfaces and explore variations of surfaces. In particular, we compute the variational derivative of the area form . and of the shape operator .. We show that the critical points of the area functional are the surfaces with mean curvature ..