Hopf manifolds and spectral geometry
HTML articles powered by AMS MathViewer
- by Kazumi Tsukada
- Trans. Amer. Math. Soc. 270 (1982), 609-621
- DOI: https://doi.org/10.1090/S0002-9947-1982-0645333-2
- PDF | Request permission
Abstract:
We characterize Hopf manifolds in the class of Hermitian manifolds by the spectra of the real Laplacians and the complex Laplacians.References
- Eric Bedford and Tatsuo Suwa, Eigenvalues of Hopf manifolds, Proc. Amer. Math. Soc. 60 (1976), 259–264. MR 418172, DOI 10.1090/S0002-9939-1976-0418172-8
- M. Berger, Le spectre des variétés riemanniennes, Rev. Roumaine Math. Pures Appl. 13 (1968), 915–931 (French). MR 239535
- Harold Donnelly, Invariance theory of Hermitian manifolds, Proc. Amer. Math. Soc. 58 (1976), 229–233. MR 407782, DOI 10.1090/S0002-9939-1976-0407782-X
- Paul Gauduchon, Fibrés hermitiens à endomorphisme de Ricci non négatif, Bull. Soc. Math. France 105 (1977), no. 2, 113–140 (French). MR 486672, DOI 10.24033/bsmf.1846
- Peter B. Gilkey, Spectral geometry and the Kaehler condition for complex manifolds, Invent. Math. 26 (1974), 231–258. MR 346849, DOI 10.1007/BF01418951
- Peter B. Gilkey, Correction to: “Spectral geometry and the Kaehler condition for complex manifolds” (Invent. Math. 26 (1974), 231–258), Invent. Math. 29 (1975), no. 1, 81–82. MR 375399, DOI 10.1007/BF01405173
- Alfred Gray, Some examples of almost Hermitian manifolds, Illinois J. Math. 10 (1966), 353–366. MR 190879
- Toyoko Kashiwada, Some properties of locally conformal Kähler manifolds, Hokkaido Math. J. 8 (1979), no. 2, 191–198. MR 551550, DOI 10.14492/hokmj/1381758270 S. Kobayashi and K. Nomizu, Foundations of differential geometry. II, Interscience, New York, 1969.
- James Morrow and Kunihiko Kodaira, Complex manifolds, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1971. MR 0302937
- 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
- Takashi Sakai, On eigen-values of Laplacian and curvature of Riemannian manifold, Tohoku Math. J. (2) 23 (1971), 589–603. MR 303465, DOI 10.2748/tmj/1178242547
- Kazumi Tsukada, Eigenvalues of the Laplacian on Calabi-Eckmann manifolds, J. Math. Soc. Japan 33 (1981), no. 4, 673–691. MR 630631, DOI 10.2969/jmsj/03340673
- Izu Vaisman, On locally conformal almost Kähler manifolds, Israel J. Math. 24 (1976), no. 3-4, 338–351. MR 418003, DOI 10.1007/BF02834764
- Izu Vaisman, Locally conformal Kähler manifolds with parallel Lee form, Rend. Mat. (6) 12 (1979), no. 2, 263–284 (English, with French summary). MR 557668
- Izu Vaisman, Remarkable operators and commutation formulas on locally conformal Kähler manifolds, Compositio Math. 40 (1980), no. 3, 287–299. MR 571051
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 270 (1982), 609-621
- MSC: Primary 53C55; Secondary 58G25
- DOI: https://doi.org/10.1090/S0002-9947-1982-0645333-2
- MathSciNet review: 645333