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Translative and Kinematic Formulae for Curvature Measures of Flat Sections
Author(s) -
Rataj Jan
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19991970107
Subject(s) - mathematics , curvature , euclidean geometry , euclidean space , space (punctuation) , mathematical analysis , geometry , pure mathematics , philosophy , linguistics
Let X be a set of positive reach in the d ‐dimensional Euclidean space. We present formulae for the integrals of the curvature measures of flat sections of X with respect to all translations/Euclidean motions of the sectioning flat. We consider the (generalized) curvature measures supported by the corresponding unit normal bundle. As a special case we obtain formulae for the spherical area measures.