Function-theoretic characterization of Einstein spaces and harmonic spaces
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- by Avner Friedman
- Trans. Amer. Math. Soc. 101 (1961), 240-258
- DOI: https://doi.org/10.1090/S0002-9947-1961-0131839-8
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References
- 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, DOI 10.1007/BF01571637 R. Courant and D. Hilbert, Methoden der mathematischen Physik, vol. 2, Berlin, Julius Springer, 1937.
- G. F. D. Duff, Partial differential equations, Mathematical Expositions, No. 9, University of Toronto Press, Toronto, 1956. MR 0078550
- Luther Pfahler Eisenhart, Riemannian Geometry, Princeton University Press, Princeton, N. J., 1949. 2d printing. MR 0035081
- Avner Friedman, Linear partial differential systems with an additional differential equation at one point, J. Math. Mech. 7 (1958), 173–190. MR 0103350, DOI 10.1512/iumj.1958.7.57015
- Sigurđur Helgason, Differential operators on homogeneous spaces, Acta Math. 102 (1959), 239–299. MR 117681, DOI 10.1007/BF02564248
- 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
- S. Minakshisundaram, Eigenfunctions on Riemannian manifolds, J. Indian Math. Soc. (N.S.) 17 (1953), 159–165 (1954). MR 61750
- J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931–954. MR 100158, DOI 10.2307/2372841
- 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. (9) 18 (1939), 217–248. MR 0000730 O. Veblen, Invariants of quadratic differential forms, Cambridge University Press, 1927.
- 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
- T. J. Willmore, Mean value theorems in harmonic Riemannian spaces, J. London Math. Soc. 25 (1950), 54–57. MR 33408, DOI 10.1112/jlms/s1-25.1.54 —, An introduction to differential geometry, Oxford University Press, 1959.
Bibliographic Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 101 (1961), 240-258
- MSC: Primary 53.70
- DOI: https://doi.org/10.1090/S0002-9947-1961-0131839-8
- MathSciNet review: 0131839