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On Gaussian and Geodesic Curvature of Riemannian Manifolds
Published online by Cambridge University Press: 20 November 2018
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In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:
Here, c is a suitable constant depending on the dimension of M and Ω is an n-form (n = dim M) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand Ω (cf. [4]).
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- Copyright © Canadian Mathematical Society 1974
References
1.
Chern, S. S., A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math.
45 (1944), 747–752.Google Scholar
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Chern, S. S., On the curvatura intégra in a Riemann manifold, Ann. of Math.
46 (1945), 674–684.Google Scholar
3.
Chern, S. S., On curvature and characteristic classes of a Riemann manifold, Abh. Math. Sem. Univ. Hamburgh (1955), 117-126.Google Scholar
4.
Greub, W. H., Zür Théorie der linear en Uebertragungen, Ann. Acad. Sci. Fenn. Ser. A. I.
846 (1964), 3–32.Google Scholar
7.
Holmann, H. and Rummler, H., Differential﹜or men, Bibliographisches Institut, Mannheim, 1972.Google Scholar
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