Download PDF by Jean-Marie Morvan: Generalized Curvatures: 2 (Geometry and Computing)

By Jean-Marie Morvan

The critical item of this ebook is the degree of geometric amounts describing N a subset of the Euclidean area (E ,), endowed with its average scalar product. allow us to country accurately what we suggest via a geometrical volume. contemplate a subset N S of issues of the N-dimensional Euclidean area E , endowed with its commonplace N scalar product. LetG be the crowd of inflexible motions of E . we are saying zero volume Q(S) linked toS is geometric with appreciate toG if the corresponding zero volume Q[g(S)] linked to g(S) equals Q(S), for all g?G . for example, the zero diameter ofS and the world of the convex hull ofS are amounts geometric with appreciate toG . however the distance from the beginning O to the nearest element ofS isn't, zero because it isn't really invariant below translations ofS. it is very important indicate that the valuables of being geometric relies on the selected team. for example, ifG is the 1 N team of projective differences of E , then the valuables ofS being a circle is geometric forG yet no longer forG , whereas the valuables of being a conic or a directly zero 1 line is geometric for bothG andG . This standpoint will be generalized to any zero 1 subsetS of any vector house E endowed with a groupG performing on it.

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Generalized Curvatures: 2 (Geometry and Computing) by Jean-Marie Morvan

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