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Examples ofsecond fundamental form
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In order to prove the existence of classical solution, we need a priori estimates for the second derivatives or equivalently, thesecondfundamentalform.
From theCambridge English Corpus
The above expression, a symmetric bilinear form at each point, is thesecondfundamentalform.
From
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This example is from Wikipedia and may be reused under a CC BY-SA license.The most important example is thesecondfundamentalform, defined classically as follows.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.It is often referred to as thesecondfundamentalform.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Observe that the mean curvature is a trace, or average, of thesecondfundamentalform, for any given component.
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This example is from Wikipedia and may be reused under a CC BY-SA license.If the affine connection is torsion-free, then thesecondfundamentalformis symmetric.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.More abstractly, the mean curvature is the trace of thesecondfundamentalformdivided by "n" (or equivalently, the shape operator).
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The eigenvalues of thesecondfundamentalform, represented in an orthonormal basis, are the principal curvatures of the surface.
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Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.