Abstract
We prove a strong variational formula for Lipschitz–Killing curvaturesof subanalytic sets. As corollaries, we reprove the Chern–Gauss–Bonnettheorem and higher Schläfli formulas. The proof of the variationalformula uses normal cycles of subanalytic sets and a new method allowinga reduction from the difficult singular geometry to computations withdifferential forms.
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Bernig, A. Variation of Curvatures of Subanalytic Spaces and Schläfli-Type Formulas. Annals of Global Analysis and Geometry 24, 67–93 (2003). https://doi.org/10.1023/A:1024269221528
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DOI: https://doi.org/10.1023/A:1024269221528