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Transactions of the American Mathematical Society

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Function-theoretic characterization of Einstein spaces and harmonic spaces


Author: Avner Friedman
Journal: Trans. Amer. Math. Soc. 101 (1961), 240-258
MSC: Primary 53.70
MathSciNet review: 0131839
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  • [1] Leifur Ásgeirsson, Über eine Mittelwertseigenschaft von Lösungen homogener linearer partieller Differentialgleichungen 2. Ordnung mit konstanten Koeffizienten, Math. Ann. 113 (1937), no. 1, 321–346 (German). MR 1513094, 10.1007/BF01571637
  • [2] R. Courant and D. Hilbert, Methoden der mathematischen Physik, vol. 2, Berlin, Julius Springer, 1937.
  • [3] G. F. D. Duff, Partial differential equations, Mathematical expositions no. 9, University of Toronto Press, Toronto, 1956. MR 0078550
  • [4] Luther Pfahler Eisenhart, Riemannian Geometry, Princeton University Press, Princeton, N. J., 1949. 2d printing. MR 0035081
  • [5] Avner Friedman, Linear partial differential systems with an additional differential equation at one point, J. Math. Mech. 7 (1958), 173–190. MR 0103350
  • [6] Sigurđur Helgason, Differential operators on homogenous spaces, Acta Math. 102 (1959), 239–299. MR 0117681
  • [7] A. Lichnerowicz, Equations de Laplace et espaces harmoniques, Premier colloque sur les équations aux dérivées partielles, Louvain, 1953, Georges Thone, Liège; Masson & Cie, Paris, 1954, pp. 9–23 (French). MR 0061873
  • [8] S. Minakshisundaram, Eigenfunctions on Riemannian manifolds, J. Indian Math. Soc. (N.S.) 17 (1953), 159–165 (1954). MR 0061750
  • [9] J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954. MR 0100158
  • [10] T. Y. Thomas and E. W. Titt, On the elementary solution of the general linear differential equation of the second order with analytic coefficients, J. Math. Pures Appl. 18 (1939), 217–248. MR 0000730
  • [11] O. Veblen, Invariants of quadratic differential forms, Cambridge University Press, 1927.
  • [12] Thomas J. Willmore, Some properties of harmonic Riemannian manifolds, Convegno Internazionale di Geometria Differenziale, Italia, 1953, Edizioni Cremonese, Roma, 1954, pp. 141–147. MR 0063106
  • [13] T. J. Willmore, Mean value theorems in harmonic Riemannian spaces, J. London Math. Soc. 25 (1950), 54–57. MR 0033408
  • [14] -, An introduction to differential geometry, Oxford University Press, 1959.

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DOI: https://doi.org/10.1090/S0002-9947-1961-0131839-8
Article copyright: © Copyright 1961 American Mathematical Society