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.
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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.
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Rataj, J., Zähle, M. General Normal Cycles and Lipschitz Manifolds of Bounded Curvature. Ann Glob Anal Geom 27, 135–156 (2005). https://doi.org/10.1007/s10455-005-5218-x
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DOI: https://doi.org/10.1007/s10455-005-5218-x