Non-compact cohomogeneity one Einstein manifolds

Christoph Böhm

Bulletin de la Société Mathématique de France (1999)

  • Volume: 127, Issue: 1, page 135-177
  • ISSN: 0037-9484

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Böhm, Christoph. "Non-compact cohomogeneity one Einstein manifolds." Bulletin de la Société Mathématique de France 127.1 (1999): 135-177. <http://eudml.org/doc/87798>.

@article{Böhm1999,
author = {Böhm, Christoph},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Einstein metric; cohomogeneity one manifold; Ricci flat metric; Ljapunov function},
language = {eng},
number = {1},
pages = {135-177},
publisher = {Société mathématique de France},
title = {Non-compact cohomogeneity one Einstein manifolds},
url = {http://eudml.org/doc/87798},
volume = {127},
year = {1999},
}

TY - JOUR
AU - Böhm, Christoph
TI - Non-compact cohomogeneity one Einstein manifolds
JO - Bulletin de la Société Mathématique de France
PY - 1999
PB - Société mathématique de France
VL - 127
IS - 1
SP - 135
EP - 177
LA - eng
KW - Einstein metric; cohomogeneity one manifold; Ricci flat metric; Ljapunov function
UR - http://eudml.org/doc/87798
ER -

References

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  1. [1] ATIYAH (M.), HITCHIN (N.). — The geometry and dynamics of magnetic monopoles. — Princeton University Press, 1988. Zbl0671.53001MR89k:53067
  2. [2] ALEKSEEVSKY (D.V.). — Classification of quaternionic spaces with a transitive solvable group of motions, Izv. Akad. Nauk SSSR Ser. Mat., t. 39, 1975; English transl. Math. USSR-Izv., t. 9, 1975, p. 297-339, p. 315-362. Zbl0324.53038
  3. [3] ALEKSEEVSKY (D.V.), KIMEL'FEL'D (B.N.). — Structure of homogeneous riemannian spaces with zero Ricci curvature, Funct. Analysis Appl., t. 9, 1975, p. 97-102. Zbl0316.53041MR53 #6466
  4. [4] BÉRARD-BERGERY (L.). — Sur de nouvelles variétés riemannienes d'Einstein, Inst. E. Cartan, t. 4, 1982, p. 1-60. Zbl0544.53038MR85b:53048
  5. [5] BESSE (A.L.). — Einstein Manifolds. — Springer-Verlag, Berlin Heidelberg, 1987. Zbl0613.53001MR88f:53087
  6. [6] BÖHM (C.). — Inhomogeneous Einstein metrics on low-dimensional spheres and other low-dimensional spaces, Invent. Math., t. 134, 1998, p. 145-176. Zbl0965.53033MR99i:53046
  7. [7] BÖHM (C.). — Non-existence of cohomogeneity one Einstein metrics, to appear in Math. Ann. Zbl0959.53020
  8. [8] BOURGUIGNON (J.-P.), KARCHER (H.). — Curvature operators: Pinching estimates and geometric examples, Ann. Sci. École Norm. Sup., t. 11, 1978, p. 71-92. Zbl0386.53031MR58 #12829
  9. [9] BREDON (G.E.). — Introduction to compact transformation groups. — Acad. Press, New York, London, 1972. Zbl0246.57017MR54 #1265
  10. [10] BRYANT (R.), SALAMON (S.). — On the construction of some complete metrics with exceptional holonomy, Duke Math. J., t. 58, 1989, p. 829-850. Zbl0681.53021MR90i:53055
  11. [11] CALABI (E.). — A construction of nonhomogeneous Einstein metrics, Differential Geometry, Proc. Symp. Pure Math., t. 27, 1975, p. 17-24. Zbl0309.53043MR52 #816
  12. [12] CALABI (E.). — Métriques kählériennes et fibrés holomorphes, Ann. Sci. École Norm. Sup., 4e série, t. 12, 1979, p. 269-294. Zbl0431.53056MR83m:32033
  13. [13] CARTAN (E.). — Sur une classe remarquable d'espaces de Riemann, Bull. Soc. Math. France, t. 54, 1926; t. 55, 1927, p. 114-134, p. 214-264. JFM53.0390.01
  14. [14] CARTAN (E.). — Sur la structure des groupes de transformations finis et continus. — Thèse, Paris, 1894. Zbl25.0638.02JFM25.0638.02
  15. [15] CHEEGER (J.), COLDING (T.H.). — Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math., t. 144, 1996, p. 189-237. Zbl0865.53037MR97h:53038
  16. [16] CHEEGER (J.), TIAN (G.). — On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay, Invent. Math., t. 118, 1994, p. 493-571. Zbl0814.53034MR95m:53051
  17. [17] DANCER (A.), WANG (M.Y.). — Kähler-Einstein manifolds of cohomogeneity one, to appear in Math. Ann. Zbl0965.53034
  18. [18] EGUCHI (T.), HANSON (A.). — Asymptotically flat self-dual solutions to Euclidean gravity, Phys. Lett. B, t. 74, 1978, p. 249-251. 
  19. [19] ESCHENBURG (J.-H.). — Lecture Notes on Symmetric spaces. — Preprint, 1997. 
  20. [20] ESCHENBURG (J.-H.), WANG (M.Y.). — The Initial Value Problem for Cohomogeneity One Einstein Metrics, to appear in J. Geom. Analysis. Zbl0992.53033
  21. [21] FERUS (D.), KARCHER (H.). — Non-rotational minimal spheres and minimizing cones, Comm. Math. Helv., t. 60, 1985, p. 247-269. Zbl0566.53052MR87a:53097
  22. [22] GALLOT (S.), HULIN (D.), LAFONTAINE (J.). — Riemannian Geometry. — Springer Verlag, New York, Berlin, Heidelberg, 1990. Zbl0716.53001MR91j:53001
  23. [23] GIBBONS (G.), PAGE (D.), POPE (C.N.). — Einstein metrics on S3, R3 and R4 bundles, Comm. Math. Phys., t. 127, 1990, p. 529-553. Zbl0699.53053MR91f:53039
  24. [24] HAWKING (S.W.). — Gravitational Instantons, Phys. Lett. A, t. 60, 1977, p. 81-83. MR57 #4965
  25. [25] HEBER (J.). — Non-compact homogeneous Einstein spaces, Invent. Math., t. 133, 1998, p. 279-352. Zbl0906.53032MR99d:53046
  26. [26] IWASAWA (K.). — On some types of topological spaces, Ann. of Math., t. 50, 1949, p. 507-558. Zbl0034.01803MR10,679a
  27. [27] JENSEN (G.R.). — Einstein metrics on principal fibre bundles, J. Differential Geometry, t. 8, 1973, p. 599-614. Zbl0284.53038MR50 #5694
  28. [28] MALGRANGE (B.). — Sur les points singuliers des équations différentielles, L'Enseignement Math., t. 20, 1974, p. 147-176. Zbl0299.34011MR51 #4316
  29. [29] MILNOR (J.). — Morse Theory. — Annals of Mathematics Studies, Princeton University Press, 1963. Zbl0108.10401MR29 #634
  30. [30] MILNOR (J.). — Curvatures of Left Invariant Metrics on Lie Groups, Advances in Math., t. 21, 1976, p. 293-329. Zbl0341.53030MR54 #12970
  31. [31] MONTGOMERY (D.), SAMELSON (H.). — Groups transitive on the n-dimensional torus, Bull. Amer. Math. Soc., t. 49, 1943, p. 455-456. Zbl0063.04078MR4,250c
  32. [32] PAGE (D.), POPE (C.N.). — Einstein metrics on quaternionic line bundles, Class. Quantum Grav., t. 3, 1986, p. 249-259. Zbl0633.53068MR87e:53079
  33. [33] PAGE (D.), POPE (C.N.). — Inhomogeneous Einstein metrics on complex line bundles, Class. Quantum Grav., t. 4, 1987, p. 213-225. Zbl0613.53020MR88f:53090
  34. [34] PERKO (L.). — Differential equations and Dynamical Systems, TAM 7. — Springer-Verlag, New York, Berlin, Heidelberg. 
  35. [35] STENZEL (M.). — Ricci-flat metrics on the complexification of a compact rank one symmetric space, Manu. Math., t. 80, 1993, p. 151-163. Zbl0811.53049MR94f:32020
  36. [36] WANG (J.). — Einstein metrics on bundles. — Ph. D. thesis, McMaster Univ., 1996. 
  37. [37] WANG (J.), WANG (M.Y.). — Einstein metrics on S2-bundles, Math. Ann., t. 310, 1998, p. 497-526. Zbl0898.53036MR99b:53072
  38. [38] WANG (M.Y.), ZILLER (W.). — Existence and non-existence of homogeneous Einstein metrics, Invent. Math., t. 84, 1986, p. 177-194. Zbl0596.53040MR87e:53081
  39. [39] WANG (M.Y.), ZILLER (W.). — On isotropy irreducible Riemannian manifolds, Acta Math., t. 166, 1991, p. 223-261. Zbl0732.53040MR92b:53078
  40. [40] WOLF (J.A.). — Spaces of constant curvature. — McGraw-Hill Series in Higher Math., 1967. Zbl0162.53304MR36 #829
  41. [41] WOLF (J.A.). — The structure of isotropy irreducible homogeneous spaces, Acta Math., t. 120, 1968 p. 59-148; correction, Acta Math., t. 152, 1984, p. 141-142. Zbl0157.52102MR36 #6549
  42. [42] ZILLER (W.). — Homogeneous Einstein Metrics on Spheres and Projective Spaces, Math. Ann., t. 259, 1982, p. 351-358. Zbl0469.53043MR84h:53062

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