Global theorems in Riemannian geometry
HTML articles powered by AMS MathViewer
- by C. B. Allendoerfer PDF
- Bull. Amer. Math. Soc. 54 (1948), 249-259
References
- Carl B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. 61 (1939), 633–644. MR 170, DOI 10.2307/2371317
- Carl B. Allendoerfer and André Weil, The Gauss-Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc. 53 (1943), 101–129. MR 7627, DOI 10.1090/S0002-9947-1943-0007627-9 3. R. Beez, Zur Theorie der Krümmungmasses von Mannigfaltigkeiten höherer Ordnung, Zeitschrift für Mathematik und Physik vol. 21 (1876) pp. 373-401.
- S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946), 776–797. MR 18022, DOI 10.1090/S0002-9904-1946-08647-4
- Shiing-shen Chern, On the curvatura integra in a Riemannian manifold, Ann. of Math. (2) 46 (1945), 674–684. MR 14760, DOI 10.2307/1969203
- Stefan Cohn-Vossen, Kürzeste Wege und Totalkrümmung auf Flächen, Compositio Math. 2 (1935), 69–133 (German). MR 1556908
- W. V. D. Hodge, The Theory and Applications of Harmonic Integrals, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1941. MR 0003947
- Sumner Byron Myers, Riemannian manifolds in the large, Duke Math. J. 1 (1935), no. 1, 39–49. MR 1545863, DOI 10.1215/S0012-7094-35-00105-3
- Sumner Byron Myers, Connections between differential geometry and topology. I. Simply connected surfaces, Duke Math. J. 1 (1935), no. 3, 376–391. MR 1545884, DOI 10.1215/S0012-7094-35-00126-0
- Sumner Byron Myers, Connections between differential geometry and topology II. Closed surfaces, Duke Math. J. 2 (1936), no. 1, 95–102. MR 1545908, DOI 10.1215/S0012-7094-36-00208-9
- S. B. Myers, Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941), 401–404. MR 4518, DOI 10.1215/S0012-7094-41-00832-3 12. A. Weil, see Allendoerfer, C. B. 13. H. Weyl, Über die Starrheit der Eiflächen und konvexen Polyeder, Preuss. Acad. Wiss. Sitzungsber. (1917) pp. 250-266.
Additional Information
- Journal: Bull. Amer. Math. Soc. 54 (1948), 249-259
- DOI: https://doi.org/10.1090/S0002-9904-1948-08965-0
- MathSciNet review: 0027171