Hello, an engineer here that is trying to understand more in topology for some mechanics ideas. It seems to me that any closed (regular) manifold in 3d Euclidean space should be able to be describe uniquely by the combination of the following 1) volume [1 real], 2) centroid [3 reals], and 3) second moments of area [9 reals cast to 7 since third axis is orthogonal to cross of 1st and 2nd]. The surface is defined of the object as C0 or higher. Can anyone give any direction as to confirming this conjecture? Is there an 11-dimensional hypersurface that is known that defines the permissible (manifold) objects in R3?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Describing 3d Manifold Objects as a Hypersurface

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