Variation of Curvatures of Subanalytic Spaces and Schläfli-Type Formulas

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.