Bergery, L.Bérard; Ikemakhen, A.
Sur l’holonomie des variétés pseudo-riemanniennes de signature (n,n)
Bulletin de la Société Mathématique de France, Tome 125 (1997) no. 1 , p. 93-114
Zbl 0916.53033 | 1 citation dans Numdam
doi : 10.24033/bsmf.2300
URL stable : http://www.numdam.org/item?id=BSMF_1997__125_1_93_0

Bibliographie

[1] Alekseevskii (D.V.). - Riemannian manifolds with exceptional holonomy groups, Funct. Anal. Appl., t. 2, (2), 1968, p. 1-10 ; english translation : Funct. Anal. Appl., t. 2, 1968, 97-105.

[2] Ambrose (W.), Singer (I.M.). - A theorem on holonomy, Trans. Amer. Math. Soc., t. 79, 1953, p. 428-443. MR 16,172b | Zbl 0052.18002

[3] Berard Bergery (L.), Ikemakhen (A.). - On the holonomy of Lorentzian Manifolds, Proceedings of Symposia in Pure Mathematics, vol. 54, (1993), part 2, p. 27-40. MR 94d:53106 | Zbl 0807.53014

[4] Berger (M.). - Sur les groupes d'holonomie des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France, t. 83, 1955, p. 279-330. Numdam | MR 18,149a | Zbl 0068.36002

[5] Berger (M.). - Les espaces symétriques non compacts, Ann. Sci. École Norm. Sup., t. 74, 1957, p. 85-177. Numdam | MR 21 #3516 | Zbl 0093.35602

[6] Besse (A. L.). - Einstein manifolds. - Springer-Verlag, Berlin-Heidelberg-New York, 1987. MR 88f:53087 | Zbl 0613.53001

[7] Brown (R.), Gray (A.). - Riemannian manifolds with holonomy group Spin(9), in Diff. Geometry in honor of K. Yano, Kinokuniya, Tokyo, 1972, p. 41-59. MR 48 #7159 | Zbl 0245.53020

[8] Bryant (R.L.). - Metrics with exceptional holonomy, Ann. of Math. (2), t. 126, 1987, p. 525-576. MR 89b:53084 | Zbl 0637.53042

[9] Bryant (R.L.). - Classical, exceptional and exotic holonomies : a status report, Actes de la table ronde de géométrie différentielle en l'honneur de M. Berger, Collection Séminaires et Congrès de la Soc. Math. France, 1, 1996, p. 93-165. MR 98c:53037 | Zbl 0882.53014

[10] Bryant (R.L.), Salamon (S. M.). - On the construction of some complete metrics with exceptional holonomy, Duke Math. J., t. 58 (3), 1989, p. 829-850. MR 90i:53055 | Zbl 0681.53021

[11] Calabi (E.). - Métriques kählériennes et fibrés holomorphes, Ann. Sci. École Norm. Sup., t. 12, 1979, p. 269-294. Numdam | MR 83m:32033 | Zbl 0431.53056

[12] Cahen (M.), Parker (M.). - Sur des classes d'espaces pseudo-riemanniens symétriques, Bull. Soc. Math. Belg., t. 22, 1970, p. 339-354. MR 44 #3247 | Zbl 0218.53067

[13] Cahen (M.), Parker (M.). - Pseudo-Riemannian symmetric spaces, Mem. Amer. Math. Soc., t. 229, 1980. MR 81b:53036 | Zbl 0438.53057

[14] Cahen (M.), Wallach (N.). - Lorentzian symmetric spaces, Bull. Amer. Math. Soc., t. 76, 1970, p. 585-591. MR 42 #2402 | Zbl 0194.53202

[15] Kobayashi (S.), Nomizu (K.). - Foundations of differential geometry. - Interscience, Wiley, New York, vol. 1, 1963 ; vol. 2, 1969. Zbl 0119.37502

[16] Ikemakhen (A.). - Examples of indecomposable non-irreducible Lorentzian manifolds, Ann. Sci. Math. Québec, t. 20, 1996, p. 53-66. MR 97e:53122 | Zbl 0873.53009

[17] Ikemakhen (A.). - Sur l'holonomie des variétés pseudo-riemanniennes de signature (2,2 + n), Preprint Université Cadi-Ayyad.

[18] Parker (M.). - Classes d'espaces pseudo-riemanniens symétriques de signature (2, n), C. R. Acad. Sci. Paris, t. 272, 1971, p. 882-884. MR 45 #2621 | Zbl 0216.18702

[19] Ruse (H.S.), Walker (A.G.) and Willmore (T.J.). - Harmonic spaces. - Edizione Cremonese, Rome, 1961. MR 25 #5456 | Zbl 0134.39202

[20] Salamon (S.). - Riemannian geometry and Holonomy groups, Pitman Research Notes in Maths, t. 201, London, Longman Scientific and Technical, 1989. MR 90g:53058 | Zbl 0685.53001

[21] Simons (J.). - On the transitivity of holonomy systems, Ann. of Math., t. 76, 1962, p. 213-234. MR 26 #5520 | Zbl 0106.15201

[22] Wu (H.). - On the de Rham decomposition theorem, Illinois J. Math., t. 8, 1964, p. 291-311. MR 28 #4488 | Zbl 0122.40005

[23] Wu (H.). - Holonomy groups of indefinite metrics, Pacific J. Math., t. 20, 1967, p. 351-392. MR 35 #3606 | Zbl 0149.39603

[24] Yau (S.T.). - On Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A., t. 74, 1977, p. 1798-1799. MR 56 #9467 | Zbl 0355.32028