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)

 
 

 

Characterizing $ S\sp m$ by the spectrum of the Laplacian on $ 2$-forms


Authors: S. I. Goldberg and H. Gauchman
Journal: Proc. Amer. Math. Soc. 99 (1987), 750-756
MSC: Primary 58G25; Secondary 53C25
DOI: https://doi.org/10.1090/S0002-9939-1987-0877051-X
MathSciNet review: 877051
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Euclidean sphere $ {S^{2n + 1}}$ is characterized by the spectrum of the Laplacian on $ 2$-forms in all dimensions.


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

  • [1] M. Berger, P. Gauduchon and E. Mazet, Le spectre d'une variété riemannienne, Lecture Notes in Math., vol. 194, Springer-Verlag, Berlin and New York, 1971. MR 0282313 (43:8025)
  • [2] R. L. Bishop and R. J. Crittenden, Geometry of manifolds, Academic Press, New York and London, 1964. MR 0169148 (29:6401)
  • [3] D. E. Blair, Contact manifolds in Riemannian geometry, Springer-Verlag, Berlin and New York, 1976. MR 0467588 (57:7444)
  • [4] B.-Y. Chen and L. Vanhecke, The spectrum of the Laplacian of Kaehler manifolds, Proc. Amer. Math. Soc. 79 (1980), 82-86. MR 560589 (81b:53042)
  • [5] S. I. Goldberg, A characterization of complex projective space, C. R. Math. Rep. Acad. Sci. Canada 6 (1984), 193-198. MR 751833 (85m:58180)
  • [6] M. Okumura, Some remarks on space with certain contact structure, Tôhoku Math. J. 14 (1962), 135-145. MR 0143148 (26:708)
  • [7] V. K. Patodi, Curvature and the fundamental solution of the heat operator, J. Indian Math. Soc. 34 (1970), 269-285. MR 0488181 (58:7744)
  • [8] S. Tanno, Eigenvalues of the Laplacian of Riemannian manifolds, Tôhoku Math. J. 25 (1973), 391-403. MR 0334086 (48:12405)
  • [9] -, The spectrum of the Laplacian for $ 1$-forms, Proc. Amer. Math. Soc. 45 (1974), 125-129. MR 0343321 (49:8063)
  • [10] G. Tsagas, The spectrum of the Laplace operator for a special Riemannian manifold, Kodai Math. J. 4 (1981), 377-382. MR 641359 (83g:58074)
  • [11] Gr. Tsagas and C. Kockinos, The geometry and the Laplace operator on the exterior $ 2$-forms on a compact Riemannian manifold, Proc. Amer. Math. Soc. 73 (1979), 109-116. MR 512069 (80b:58068)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G25, 53C25

Retrieve articles in all journals with MSC: 58G25, 53C25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0877051-X
Keywords: Spectrum of the Laplacian, contact Riemannian manifold
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society