The spectrum of the Laplacian of Kähler manifolds
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- by Bang-Yen Chen and Lieven Vanhecke PDF
- Proc. Amer. Math. Soc. 79 (1980), 82-86 Request permission
Abstract:
We strengthen some results on the spectrum of the Laplacian for 0- and 1-forms [8], [9] on Kähler manifolds and give some new results for the 2-forms.References
- Marcel Berger, Paul Gauduchon, and Edmond Mazet, Le spectre d’une variété riemannienne, Lecture Notes in Mathematics, Vol. 194, Springer-Verlag, Berlin-New York, 1971 (French). MR 0282313, DOI 10.1007/BFb0064643
- R. L. Bishop and S. I. Goldberg, Rigidity of positively curved Kaehler manifolds, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1037–1041. MR 195112, DOI 10.1073/pnas.54.4.1037
- Bang-yen Chen, Characterizations of Einstein Kaehler manifolds and applications, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 61 (1976), no. 6, 592–595 (1977) (English, with Italian summary). MR 500756
- Samuel I. Goldberg and Shoshichi Kobayashi, Holomorphic bisectional curvature, J. Differential Geometry 1 (1967), 225–233. MR 227901
- Alain Lascoux and Marcel Berger, Variétés Kähleriennes compactes, Lecture Notes in Mathematics, Vol. 154, Springer-Verlag, Berlin-New York, 1970 (French). MR 0278248, DOI 10.1007/BFb0069331
- Koichi Ogiue, Generalized scalar curvatures of cohomological Einstein Kaehler manifolds, J. Differential Geometry 10 (1975), 201–205. MR 375187
- V. K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970), no. 3-4, 269–285 (1971). MR 0488181
- Shǔkichi Tanno, Eigenvalues of the Laplacian of Riemannian manifolds, Tǒhoku Math. J. (2) 25 (1973), 391–403. MR 0334086, DOI 10.2748/tmj/1178241341
- Shûkichi Tanno, The spectrum of the Laplacian for $1$-forms, Proc. Amer. Math. Soc. 45 (1974), 125–129. MR 343321, DOI 10.1090/S0002-9939-1974-0343321-8
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 82-86
- MSC: Primary 53C55; Secondary 58G25
- DOI: https://doi.org/10.1090/S0002-9939-1980-0560589-6
- MathSciNet review: 560589