This is a preview of subscription content, log in via an institution to check access.
References
Baird, P.: Harmonic maps with symmetry, harmonic morphisms and deformations of metrics. Research Notes in Mathematics, Vol. 87, Boston London Melbourne: Pitman 1983
Baird, P.: Harmonic morphisms onto Riemann surfaces and generalized analytic functions. Ann. Inst. Fourier, Grenoble37, 135–173 (1987)
Baird, P., Eells, J.: A conservation law for harmonic maps. In: Looijenga, E., Siersma, D., Takens, F. (eds.). Geometry Symposium Utrecht 1980, Proceedings. Lecture Notes Mathematics, Vol. 894, pp. 1–25. Berlin Heidelberg New York: Springer 1981
Bernard, A., Campbell, E.A., Davie, A.M.: Brownian motion and generalized analytic and inner functions. Ann. Inst. Fourier, Grenoble29, 207–228 (1979)
Chern, S.S.: Minimal surfaces in an Euclidean space ofN dimensions. In: Cairns, S.S. (ed.) Differential and combinatorial topology, pp. 187–198 Princeton: Princeton University Press 1965
Conway, J.B.: Functions of one complex variable. Berlin Heidelberg New York: Springer 1983
Eells, J., Polking, J.C.: Removable singularities of harmonic maps. Indiana Univ. Math. J.33, 859–871 (1984)
Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds. Am. J. Math.86, 109–160 (1964)
Fuglede, B.: Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier Grenoble28, 107–144 (1978)
Greene, R.E., Wu, H.: Embeddings of open Riemannian manifolds by harmonic functions. Ann. Inst. Fourier, Grenoble12, 415–571 (1962)
Helms, L.L.: Introduction to potential theory. New York London Sydney Toronto: Wiley 1969
Hoffman, D.A., Osserman, R.: The geometry of the generalized Gauss map. Memoirs of the American Math. Soc., Vol. 28, No. 236. Providence: Am. Math. Soc. 1980
Ishihara, T.: A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Kyoto Univ.19, 215–229 (1979)
Jacobi, C.G.J.: Über eine particuläre Lösung der partiellen Differentialgleichung\(\frac{{\partial ^2 V}}{{\partial x^2 }} + \frac{{\partial ^2 V}}{{\partial y^2 }} + \frac{{\partial ^2 V}}{{\partial z^2 }} = 0\). Crelle Reine Angew. Math.36, 113–134 (1847)
Kamber, F.W., Tondeur, Ph.: The Bernstein problem for foliations. In: Global differential geometry and global analysis. Proceedings Berlin 1984. Lecture Notes Mathematics, Vol. 1156, pp. 216–218 Berlin Heidelberg New York: Springer 1985
Osserman, R.: A survey of minimal surfaces. New York: Van Nostrand Reinhold 1969. Secd. edit.: New York: Dover 1986
Reinhart, B.L.: Differential geometry of foliations. Ergebnisse Math., Vol. 99. Berlin Heidelberg New York: Springer 1983
Ruh, E.A., Vilms, J.: The tension field of the Gauss map. Trans. Am. Math. Soc.149, 569–573 (1970)
Siegel, C.L.: Topics in complex function theory. New York London Sydney Toronto: Wiley 1969
Steenrod, N.: The topology of fibre bundles. Princeton: Princeton University Press 1951
Vaisman, I.: Conformal foliations. Kodai Math. J.2, 26–37 (1979)
Wolf, J.: Spaces of constant curvature. New York St. Louis San Francisco Toronto London Sydney: McGraw-Hill 1967
Wood, J.C.: The Gauss map of a harmonic morphism. In: Cordero, L.A. (ed.) Differential geometry. Research Notes Mathematics, Vol. 131, pp. 149–155. Boston London Melbourne: Pitman 1985
Wood, J.C.: Harmonic morphisms, foliations and Gauss maps. In: Siu, Y.T. (ed.) Complex differential geometry and nonlinear differential equations. Contemporary Mathematics, Vol. 49, pp. 145–183. Providence: Am. Math. Soc. 1986
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baird, P., Wood, J.C. Bernstein theorems for harmonic morphisms from R3 andS 3 . Math. Ann. 280, 579–603 (1988). https://doi.org/10.1007/BF01450078
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01450078