Elliptic operators and a theorem of Poincaré
HTML articles powered by AMS MathViewer
- by Leon Karp PDF
- Proc. Amer. Math. Soc. 95 (1985), 649-652 Request permission
Abstract:
A general vanishing theorem is proved for elliptic operators. This result is then used to give a simple proof of the fact that the arithmetic genus vanishes for complex manifolds of odd dimension $n$ with nowhere zero $\left ( {n,0} \right )$ form.References
- N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) 36 (1957), 235–249. MR 92067
- M. F. Atiyah and I. M. Singer, The index of elliptic operators. I, Ann. of Math. (2) 87 (1968), 484–530. MR 236950, DOI 10.2307/1970715
- F. Hirzebruch, Topological methods in algebraic geometry, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 131, Springer-Verlag New York, Inc., New York, 1966. New appendix and translation from the second German edition by R. L. E. Schwarzenberger, with an additional section by A. Borel. MR 0202713
- A. Hurwitz, Ueber algebraische Gebilde mit eindeutigen Transformationen in sich, Math. Ann. 41 (1892), no. 3, 403–442 (German). MR 1510753, DOI 10.1007/BF01443420 L. Karp, Vector fields on manifolds, Thesis, New York University, 1976. R. Narasimhan, Analysis on real and complex manifolds, North-Holland, Amsterdam, 1973.
- Richard S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies, No. 57, Princeton University Press, Princeton, N.J., 1965. With contributions by M. F. Atiyah, A. Borel, E. E. Floyd, R. T. Seeley, W. Shih and R. Solovay. MR 0198494, DOI 10.1515/9781400882045
- Edward Witten, Supersymmetry and Morse theory, J. Differential Geometry 17 (1982), no. 4, 661–692 (1983). MR 683171
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 649-652
- MSC: Primary 58A10; Secondary 32J99
- DOI: https://doi.org/10.1090/S0002-9939-1985-0810179-7
- MathSciNet review: 810179