Vector fields and Gauss-Bonnet
HTML articles powered by AMS MathViewer
- by Paul F. Baum PDF
- Bull. Amer. Math. Soc. 76 (1970), 1202-1211
References
- M. F. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes. I, Ann. of Math. (2) 86 (1967), 374–407. MR 212836, DOI 10.2307/1970694
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. III, Ann. of Math. (2) 87 (1968), 546–604. MR 236952, DOI 10.2307/1970717
- Paul F. Baum and Raoul Bott, On the zeros of meromorphic vector-fields, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. 29–47. MR 0261635
- Paul Baum and Jeff Cheeger, Infinitesimal isometries and Pontryagin numbers, Topology 8 (1969), 173–193. MR 238351, DOI 10.1016/0040-9383(69)90008-1
- Raoul Bott, Vector fields and characteristic numbers, Michigan Math. J. 14 (1967), 231–244. MR 211416
- Raoul Bott, A residue formula for holomorphic vector-fields, J. Differential Geometry 1 (1967), 311–330. MR 232405
- Raoul Bott, On a topological obstruction to integrability, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 127–131. MR 0266248
- Raoul Bott and S. S. Chern, Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections, Acta Math. 114 (1965), 71–112. MR 185607, DOI 10.1007/BF02391818
- Shiing-shen Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math. (2) 45 (1944), 747–752. MR 11027, DOI 10.2307/1969302
- Shiing-shen Chern, Characteristic classes of Hermitian manifolds, Ann. of Math. (2) 47 (1946), 85–121. MR 15793, DOI 10.2307/1969037
- Shiing-shen Chern, Differential geometry of fiber bundles, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R.I., 1952, pp. 397–411. MR 0045432
- Harley Flanders, Differential forms, Studies in Global Geometry and Analysis, Math. Assoc. America, Buffalo, N.Y.; distributed by Prentice-Hall, Englewood Cliffs, N.J., 1967, pp. 57–95. MR 0212717
- Phillip A. Griffiths, On a theorem of Chern, Illinois J. Math. 6 (1962), 468–479. MR 144360
- Noel J. Hicks, Notes on differential geometry, Van Nostrand Mathematical Studies, No. 3, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. MR 0179691 15. H. Hopf, Vectorfelder in n-dimensionalen Mannigfaltigkeiten, Math. Ann. 96 (1926), 225-250.
- John W. Milnor, Topology from the differentiable viewpoint, University Press of Virginia, Charlottesville, Va., 1965. Based on notes by David W. Weaver. MR 0226651
- Barrett O’Neill, Elementary differential geometry, Academic Press, New York-London, 1966. MR 0203595 18. J. Pasternack, Thesis, Princeton University, Princeton, N. J., 1970.
Additional Information
- Journal: Bull. Amer. Math. Soc. 76 (1970), 1202-1211
- MSC (1970): Primary 57D25, 57D20, 32C10; Secondary 57D30, 53C05
- DOI: https://doi.org/10.1090/S0002-9904-1970-12607-6
- MathSciNet review: 0266255