Get Generalized Curvatures: 2 (Geometry and Computing) PDF

By Jean-Marie Morvan

ISBN-10: 354073791X

ISBN-13: 9783540737919

ISBN-10: 3642093000

ISBN-13: 9783642093005

The relevant item of this e-book is the degree of geometric amounts describing N a subset of the Euclidean house (E ,), endowed with its regular scalar product. allow us to kingdom accurately what we suggest by way of a geometrical volume. ponder a subset N S of issues of the N-dimensional Euclidean area E , endowed with its average N scalar product. LetG be the crowd of inflexible motions of E . we are saying zero volume Q(S) linked toS is geometric with recognize 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 realm of the convex hull ofS are amounts geometric with appreciate toG . however the distance from the starting place O to the nearest aspect ofS isn't really, zero because it isn't really invariant less than translations ofS. you will need to indicate that the valuables of being geometric will depend on the selected staff. for example, ifG is the 1 N crew of projective variations of E , then the valuables ofS being a circle is geometric forG yet now not forG , whereas the valuables of being a conic or a instantly zero 1 line is geometric for bothG andG . This standpoint should 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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