Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1975-0355914-3
MathSciNet review: 0355914
Full-text PDF Free Access

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, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R. I., 1970, pp. 121-125. MR 41 #9141. 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 Gilkey, Spectral geometry and the Kaehler condition for complex manifolds (to appear). MR 0346849 (49:11571)
  • [4] V. K. Patodi, An analytic proof of the Riemann-Roch-Hirzebruch theorem for Kaehler manifolds, J. Differential Geometry 5 (1971), 251-283. MR 44 #7502. MR 0290318 (44:7502)
  • [5] -, Curvature and the eigenforms of the Laplace operator, J. Differential Geometry 5 (1971), 233-249. MR 45 #1201. MR 0292114 (45:1201)
  • [6] E. Vesentini, Lectures on Levi convexity and cohomology vanishing theorems, Tata Inst. of Fund. Res. Lect. on Math., no. 39, Tata Institute of Fundamental Research, Bombay, 1967. MR 38 #342. MR 0232016 (38:342)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355914-3
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society