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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A spectral condition determining the Kaehler property


Author: Harold Donnelly
Journal: Proc. Amer. Math. Soc. 47 (1975), 187-194
MathSciNet review: 0355914
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Abstract | References | Additional Information

Abstract: We prove that the spectrum of the reduced complex Laplacian determines if a Hermitian manifold is Kaehler.


References [Enhancements On Off] (What's this?)

  • [1] Marcel Berger, Eigenvalues of the Laplacian, Global Analysis (Proc. Sympos. Pure Math., Vol. XVI, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 121–125. MR 0264549 (41 #9141)
  • [2] Harold Donnelly, Minakshisundaram's coefficients on Kaehler manifolds, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc., Providence, R. I. (to appear).
  • [3] Peter B. Gilkey, Spectral geometry and the Kaehler condition for complex manifolds, Invent. Math. 26 (1974), 231–258. MR 0346849 (49 #11571)
  • [4] V. K. Patodi, An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds, J. Differential Geometry 5 (1971), 251–283. MR 0290318 (44 #7502)
  • [5] V. K. Patodi, Curvature and the eigenforms of the Laplace operator, J. Differential Geometry 5 (1971), 233–249. MR 0292114 (45 #1201)
  • [6] E. Vesentini, Lectures on Levi convexity of complex manifolds and cohomology vanishing theorems, Notes by M. S. Raghunathan. Tata Institute of Fundamental Research Lectures on Mathematics, No. 39, Tata Institute of Fundamental Research, Bombay, 1967. MR 0232016 (38 #342)


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0355914-3
PII: S 0002-9939(1975)0355914-3
Article copyright: © Copyright 1975 American Mathematical Society