Euclidean 3-manifold 
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Wikipedia
https://en.wikipedia.org › wiki › 3-manifold
euclidean 3-manifold from en.wikipedia.org
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the ...
Important examples of 3... ·
Some important structures on... · Foundational results
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Contact geometry
Contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle and specified by a one-form, both of which satisfy a 'maximum non-degeneracy' condition called 'complete non-integrability'. From the Frobenius theorem, one recognizes the condition as the opposite of the condition that the distribution be determined by a codimension one foliation on the manifold ('complete integrability').
Contact geometry is in many ways an odd-dimensional counterpart of symplectic geometry, which belongs to the even-dimensional world. Both contact and symplectic geometry are motivated by the mathematical formalism of classical mechanics, where one can consider either the even-dimensional phase space of a mechanical system or the odd-dimensional extended phase space that includes the time variable.
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double cube space
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