, Volume 27, Issue 2, pp 135-156

General Normal Cycles and Lipschitz Manifolds of Bounded Curvature

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Abstract

Closed Legendrian (d − 1)-dimensional locally rectifiable currents on the sphere bundle in \(\mathbb{R}\) d are considered and the associated index functions are studied. A topological condition assuring the validity of a local version of the Gauss–Bonnet formula is established. The case of lower-dimensional Lipschitz submanifolds in \(\mathbb{R}\) d and their associated normal cycles is examined in detail.

Supported by the Grant Agency of Charles University, Project No. 283/2003/B-MAT/MFF, and by the Czech Ministry of Education, project MSM 113200007.