Generalized Curvatures Ebook

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The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space E endowed with its standard scalar product Let us state precisely what we mean by a geometric quantity Consider a subset N S of points of the N-dimensional Euclidean space E endowed with its standard N scalar product LetG be the group of rigid motions of E We say that a 0 quantity QS associated toS is geometric with respect toG if the corresponding 0 quantity QgS associated to gS equals QS for all gG For instance the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG But the distance from the origin O to the closest point ofS is not 0 since it is not invariant under translations ofS It is important to point out that the property of being geometric depends on the chosen group For instance ifG is the 1 N group of projective transformations of E then the property ofS being a circle is geometric forG but not forG while the property of being a conic or a straight 0 1 line is geometric for bothG andG This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on itGeneralized Curvatures EbookBy Jean-Marie Morvan Publisher Springer Print ISBN 9783540737919 354073791X eText ISBN 9783540737926 3540737928 Copyright year 2008 Format PDF Available from 12900 USD SKU 9783540737926

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9783540737919

The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space E endowed with its standard scalar product Let us state precisely what we mean by a geometric quantity Consider a subset N S of points of the N-dimensional Euclidean space E endowed with its standard N scalar product LetG be the group of rigid motions of E We say that a 0 quantity QS associated toS is geometric with respect toG if the corresponding 0 quantity QgS associated to gS equals QS for all gG For instance the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG But the distance from the origin O to the closest point ofS is not 0 since it is not invariant under translations ofS It is important to point out that the property of being geometric depends on the chosen group For instance ifG is the 1 N group of projective transformations of E then the property ofS being a circle is geometric forG but not forG while the property of being a conic or a straight 0 1 line is geometric for bothG andG This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on itGeneralized Curvatures EbookBy Jean-Marie Morvan Publisher Springer Print ISBN 9783540737919 354073791X eText ISBN 9783540737926 3540737928 Copyright year 2008 Format PDF Available from 12900 USD SKU 9783540737926