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Manifolds of Riemannian metrics with prescribed scalar curvature
Authors:
Arthur E. Fischer and Jerrold E. Marsden
Journal:
Bull. Amer. Math. Soc. 80 (1974), 479-484
MSC (1970):
Primary 53C25, 58D15; Secondary 35J60, 58G99, 47H15
MathSciNet review:
0346839
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
M.
Berger and D.
Ebin, Some decompositions of the space of symmetric tensors on a
Riemannian manifold, J. Differential Geometry 3
(1969), 379–392. MR 0266084
(42 #993)
- 2.
Dieter
R. Brill and Stanley
Deser, Instability of closed spaces in general relativity,
Comm. Math. Phys. 32 (1973), 291–304. MR 0329548
(48 #7890)
- 3.
David
G. Ebin, The manifold of Riemannian metrics, Global Analysis
(Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), Amer. Math.
Soc., Providence, R.I., 1970, pp. 11–40. MR 0267604
(42 #2506)
- 4.
Arthur
E. Fischer and Jerrold
E. Marsden, Linearization stability of the
Einstein equations, Bull. Amer. Math. Soc.
79 (1973),
997–1003. MR 0426035
(54 #13981), http://dx.doi.org/10.1090/S0002-9904-1973-13299-9
- 5.
Arthur
E. Fischer and Jerrold
E. Marsden, Manifolds of Riemannian metrics with
prescribed scalar curvature, Bull. Amer. Math.
Soc. 80 (1974),
479–484. MR 0346839
(49 #11561), http://dx.doi.org/10.1090/S0002-9904-1974-13457-9
- 6.
Arthur
E. Fischer and Joseph
A. Wolf, The Calabi construction for compact
Ricci flat Riemannian manifolds, Bull. Amer.
Math. Soc. 80
(1974), 92–97. MR 0383299
(52 #4180), http://dx.doi.org/10.1090/S0002-9904-1974-13368-9
- 7.
Arthur
E. Fischer and Joseph
A. Wolf, The structure of compact Ricci-flat Riemannian
manifolds, J. Differential Geometry 10 (1975),
277–288. MR 0377759
(51 #13928)
- 8.
Jerry
L. Kazdan and F.
W. Warner, Curvature functions for 2-manifolds
with negative Euler characteristic, Bull. Amer.
Math. Soc. 78
(1972), 570–574. MR 0320947
(47 #9480), http://dx.doi.org/10.1090/S0002-9904-1972-13006-4
- 9.
Jerry
L. Kazdan and F.
W. Warner, Curvature functions for 2-manifolds, Partial
differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ.
California, Berkeley, Calif., 1971), Amer. Math. Soc., Providence, R.I.,
1973, pp. 387–392. MR 0343207
(49 #7951)
- 10.
André
Lichnerowicz, Propagateurs et commutateurs en relativité
générale, Inst. Hautes Études Sci. Publ. Math.
10 (1961), 56 (French). MR 0157736
(28 #967)
- 11.
André
Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris
257 (1963), 7–9 (French). MR 0156292
(27 #6218)
- 12.
Jürgen
Moser, On the volume elements on a
manifold, Trans. Amer. Math. Soc. 120 (1965), 286–294. MR 0182927
(32 #409), http://dx.doi.org/10.1090/S0002-9947-1965-0182927-5
- 13.
Morio
Obata, Certain conditions for a Riemannian manifold to be isometric
with a sphere, J. Math. Soc. Japan 14 (1962),
333–340. MR 0142086
(25 #5479)
- 14.
Joseph
A. Wolf, Spaces of constant curvature, 2nd ed., Department of
Mathematics, University of California, Berkeley, Calif., 1972. MR 0343213
(49 #7957)
- 1.
- M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379-392. MR 42 #993. MR 266084
- 2.
- D. Brill and S. Deser, Instability of closed spaces in general relativity, Comm. Math. Phys. 32 (1973), 291-304. MR 329548
- 3.
- D. Ebin, The manifold of Riemannian metrics, Proc. Sympos. Pure Math., vol. 15, Amer. Math. Soc. Providence, R.I., 1970, pp. 11-40. MR 42 #2506. MR 267604
- 4.
- A. Fischer and J. Marsden, Linearization stability of the Einstein equations, Bull. Amer. Math. Soc. 79 (1973), 995-1001. MR 426035
- 5.
- A. Fischer and J. Marsden, The manifold of Riemannian metrics with prescribed scalar curvature (to appear). MR 346839
- 6.
- A. Fischer and J. Wolf, The Calabi construction for compact Ricci-flat Riemannian manifolds, Bull. Amer. Math. Soc. 80 (1974), 92-97. MR 383299
- 7.
- A. Fischer and J. Wolf, The structure of compact Ricci-flat Riemannian manifolds (to appear). MR 377759
- 8.
- J. Kazdan and F. Warner, Curvature functions for compact 2-manifolds, Ann. of Math. (to appear); See also: Bull. Amer. Math. Soc. 78 (1972), 570-574. MR 320947
- 9.
- J. Kazdan and F. Warner, Prescribing curvatures, AMS Summer Institute on Differential Geometry, Stanford (1973) (preprint). MR 343207
- 10.
- A. Lichnerowicz, Propagateurs et commutateurs en relativité générale Inst. Hautes Études Sci. Publ. Math. No. 10 (1961), 56 pp. MR 28 #967. MR 157736
- 11.
- A. Lichnerowicz, Spineurs harmoniques, C. R. Acad. Sci. Paris 257 (1963), 7-9. MR 27 #6218. MR 156292
- 12.
- J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. MR 32 #409. MR 182927
- 13.
- M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333-340. MR 25 #5479. MR 142086
- 14.
- J. A. Wolf, Spaces of constant curvature, 2d ed., J. A. Wolf, Berkeley, Calif., 1972. MR 343213
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1974-13457-9
PII:
S 0002-9904(1974)13457-9
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