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A direct approach to the determination of Gaussian and scalar curvature functions. (English) Zbl 0297.53021


MSC:

53C20 Global Riemannian geometry, including pinching
35J60 Nonlinear elliptic equations
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
58J99 Partial differential equations on manifolds; differential operators
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References:

[1] Bourguignon, J.-P.: Thesis, University of Paris VII, 1974
[2] Chern, S.S.: Differentiable Manifolds (Lecture Notes), Department of Mathematics, University of Chicago, Chicago, Ill., 1959 · Zbl 0099.37402
[3] ElĂ­asson, H.: On variations of Metrics. Math. Scand,29, 317-327 (1971)
[4] Fischer, A., Marsden, J.: Submanifolds of Riemannian metrics with Prescribed Scalar Curvature. Proc. of Symposia in Pure Math.27, Amer. Math. Soc. (to appear) · Zbl 0288.53040
[5] Hitchin, N.: The Space of Harmonic Spinors. Advances in Math.14, 1-55 (1974) · Zbl 0284.58016
[6] Kazdan, Jerry, L., Warner, F.W.: Curvature Functions for Compact 2-Manifolds. Annals of Math.99, 14-47 (1974) · Zbl 0273.53034
[7] Kazdan, Jerry L., Warner, F.W.: Curvature Functions for Open 2-Manifolds. Annals of Math.99, 203-219 (1974) · Zbl 0278.53031
[8] Kazdan, Jerry L., Warner, F.W.: Scalar Curvature and Conformal Deformation of Riemannian Structure. J. Diff. Geo.10 (1975). To appear · Zbl 0296.53037
[9] Kazdan, Jerry L., Warner, F.W.: Existence and Conformal Deformation of Metrics with Prescribed Gaussian and Scalar Curvature. To appear in Annals of Math. · Zbl 0297.53020
[10] Kazdan, Jerry L., Warner, F.W.: Prescribing Curvatures. Proc. of Symposia in Pure Math.27 (Differential Geometry), Amer. Math. Soc. To appear · Zbl 0313.53017
[11] Lichnerowicz, A.: Spineurs harmoniques. C.R. Acad. Sci. Paris257, 7-9 (1963) · Zbl 0136.18401
[12] Moser, J.: On a Nonlinear problem in Differential Geometry. Dynamical Systems (M. Peixoto, ed.). New York: Academic Press 1973 · Zbl 0275.53027
[13] Spivac, M.: A Comprehensive introduction to differential geometry, III. Boston: Publish or Perish 1975
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