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How can 5 sticks with coinciding ends be organized in space this sort of that they're at their most angles to each other?

For every sequence of nonempty open up sets You will find there's disjoint sequence of nonempty open up sets "down below" it

In any arbitrary curvilinear coordinate system and in some cases while in the absence of a metric over the manifold, the Levi-Civita symbol as defined previously mentioned could be thought to be a tensor density field in two different ways.

In Einstein notation, the duplication of the i index implies the sum on i. The past is then denoted εijkεimn = δjmδkn − δjnδkm.

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On a pseudo-Riemannian manifold, 1 may perhaps outline a coordinate-invariant covariant tensor field whose coordinate representation agrees With all the Levi-Civita image anywhere the coordinate system is these that the basis with the tangent Area is orthonormal with respect into the metric and matches a particular orientation.

in which gab would be the illustration from the metric in that coordinate method. We can easily likewise contemplate a contravariant Levi-Civita tensor by increasing the indices With more info all the metric as regular,

Up to 3 sets of CTs for each phase can be paralleled for every meter without the require to get a meter multiplier