$L^{2}$ harmonic forms on rotationally symmetric Riemannian manifolds
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- by Jozef Dodziuk
- Proc. Amer. Math. Soc. 77 (1979), 395-400
- DOI: https://doi.org/10.1090/S0002-9939-1979-0545603-8
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Abstract:
The paper contains a vanishing theorem for ${L^2}$ harmonic forms on complete rotationally symmetric Riemannian manifolds. This theorem requires no assumptions on curvature.References
- M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l’Honneur de Henri Cartan (Orsay, 1974) Astérisque, No. 32-33, Soc. Math. France, Paris, 1976, pp. 43–72. MR 0420729
- Shiing Shen Chern, Differential geometry: its past and its future, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 41–53. MR 0428217
- R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 521983, DOI 10.1007/BFb0063413
- John Milnor, On deciding whether a surface is parabolic or hyperbolic, Amer. Math. Monthly 84 (1977), no. 1, 43–46. MR 428232, DOI 10.2307/2318308 G. de Rham, Variétés différentiables, formes, courants, formes harmoniques, 2nd ed., Actualités Sci. Indust., no. 1222a, Hermann, Paris, 1960.
- J. J. Stoker, Differential geometry, Pure and Applied Mathematics, Vol. XX, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1969. MR 0240727
Bibliographic Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 395-400
- MSC: Primary 58A14; Secondary 53C99, 58G99
- DOI: https://doi.org/10.1090/S0002-9939-1979-0545603-8
- MathSciNet review: 545603