Annals of Global Analysis and Geometry

, Volume 27, Issue 2, pp 135–156

General Normal Cycles and Lipschitz Manifolds of Bounded Curvature

Article

DOI: 10.1007/s10455-005-5218-x

Cite this article as:
Rataj, J. & Zähle, M. Ann Glob Anal Geom (2005) 27: 135. doi:10.1007/s10455-005-5218-x

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.

Lipschitz manifold normal cycle curvature measure Gauss–Bonnet formula principal kinematic formula 

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mathematical InstituteCharles UniversityPraha 8Czech Republic
  2. 2.Mathematical InstituteFriedrich-Schiller-UniversityJenaGermany

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