SWhat changed
Chern gives an intrinsic differential-form proof that integrates curvature to the Euler characteristic for closed oriented even-dimensional Riemannian manifolds, avoiding the earlier proof's use of local Euclidean embeddings.
Scientific scope
Chern gives an intrinsic differential-form proof that integrates curvature to the Euler characteristic for closed oriented even-dimensional Riemannian manifolds, avoiding the earlier proof's use of local Euclidean embeddings. Exact 1944 Annals 45(4),747-752 original: all six article pages/PDF 2-7 text and footnotes read, PDF 1 archive cover metadata only. Closed orientable even-dimensional Riemannian manifold, with the differentiability/metric regularity stated in the paper; no boundary/noncompact/odd-dimensional or lowered-regularity extension imported. Curvature top form is pulled back to the unit tangent sphere bundle, where transgression makes it exact; it is not claimed exact on the closed base. Vector-field index theorem and Stokes are inherited. General formula already attributed in the introduction to Allendoerfer/Weil; Chern supplies an intrinsic proof, not sole first discovery of all cases. Later polyhedral extensions, all Chern/characteristic classes, index theory and downstream applications separate. The complete symbolic proof and its coefficients have not been independently reconstructed or certified here. independent scientific/calibration certification NONE.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Shiing-Shen Chern · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Chern, A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds, Annals 45(4),747-752(1944), original scan
- Publisher-deposited Crossref identity for Chern 1944 intrinsic proof
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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