Recent advances in the theory of holonomy
Séminaire Bourbaki : volume 1998/99, exposés 850-864, Astérisque, no. 266 (2000), Exposé no. 861, 24 p.

Voir la notice du chapitre de livre provenant de la source Numdam

MR   Zbl   EuDML

Bryant, Robert. Recent advances in the theory of holonomy, dans Séminaire Bourbaki : volume 1998/99, exposés 850-864, Astérisque, no. 266 (2000), Exposé no. 861, 24 p.. http://geodesic.mathdoc.fr/item/SB_1998-1999__41__351_0/
@incollection{SB_1998-1999__41__351_0,
     author = {Bryant, Robert},
     title = {Recent advances in the theory of holonomy},
     booktitle = {S\'eminaire Bourbaki : volume 1998/99, expos\'es 850-864},
     series = {Ast\'erisque},
     note = {talk:861},
     pages = {351--374},
     year = {2000},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {266},
     mrnumber = {1772679},
     zbl = {1014.53029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SB_1998-1999__41__351_0/}
}
TY  - CHAP
AU  - Bryant, Robert
TI  - Recent advances in the theory of holonomy
BT  - Séminaire Bourbaki : volume 1998/99, exposés 850-864
AU  - Collectif
T3  - Astérisque
N1  - talk:861
PY  - 2000
SP  - 351
EP  - 374
IS  - 266
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/SB_1998-1999__41__351_0/
LA  - en
ID  - SB_1998-1999__41__351_0
ER  - 
%0 Book Section
%A Bryant, Robert
%T Recent advances in the theory of holonomy
%B Séminaire Bourbaki : volume 1998/99, exposés 850-864
%A Collectif
%S Astérisque
%Z talk:861
%D 2000
%P 351-374
%N 266
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/SB_1998-1999__41__351_0/
%G en
%F SB_1998-1999__41__351_0

[Al1] D. Alekseevskii - Riemannian spaces with unusual holonomy groups, Funct. Anal. Appl. 2 (1968), 97-105. | Zbl | MR

[Al2] D. Alekseevskii - Classification of quaternionic spaces with a transitive solvable group of motions, Math. USSR-Izv 9 (1975), 297-339. | Zbl

[AS] A. Ambrose and I. Singer - A theorem on holonomy, Trans. Amer. Math. Soc. 75 (1953), 428-443. | Zbl | MR

[BB] L. Bérard-Bergery - On the holonomy of Lorentzian manifolds, Proc. Symp. Pure Math. 54 (1993), 27-40. | Zbl | MR

[BI] L. Bérard-Bergery and A. Ikemakhen - Sur l'holonomie des variétés pseudo-riemanniennes de signature ( n , n ) , Bull. Soc. Math. France 125 (1997), 93-114. | Zbl | MR | Numdam

[Ber1] M. Berger, Sur les groupes d'holonomie des variétés à connexion affine et des variétés riemanniennes, Bull. Soc. Math. France 83 (1955), 279-330. | Zbl | MR | Numdam

[Ber2] M. Berger - Les espaces symétriques non compacts, Ann. Sci. École Norm. Sup. 74 (1957), 85-177. | Zbl | MR | Numdam

[Bes] A. Besse - Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 10, Springer-Verlag, Berlin, 1987. | Zbl | MR

[BL] A. Borel and A. Lichnerowicz - Groupes d'holonomie des variétés riemanniennes, C.R. Acad. Sci. Paris 234 (1952), 1835-1837. | Zbl | MR

[BG] R. Brown and A. Gray - Riemannian manifolds with holonomy group Spin ( 9 ) , in Differential Geometry (in honor of Kentaro Yano), Kinokuniya, Tokyo, 1972, 41-59. | Zbl | MR

[Br1] R. Bryant - Metrics with exceptional holonomy, Ann. Math. 126 (1987), 525- 576. | Zbl | MR

[Br2] R. Bryant - Two exotic holonomies in dimension four, path geometries, and twistor theory, Amer. Math. Soc. Proc. Symp. Pure Math. 53 (1991), 33-88. | Zbl | MR

[Br3] R. Bryant - Classical, exceptional, and exotic holonomies: a status report, in Actes de la Table Ronde de Géométrie Différentielle en l'Honneur de Marcel Berger, Soc. Math. France, 1996, 93-166. | Zbl | MR

[BCG] R. Bryant, et al - Exterior Differential Systems, MSRI Series 18, Springer-Verlag, 1991. | Zbl | MR

[BS] R. Bryant and S. Salamon - On the construction of some complete metrics with exceptional holonomy, Duke Math. J. 58 (1989), 829-850. | Zbl | MR

[Ca1] É. Cartan - La Géometrie des Espaces de Riemann, Memorial des SciencesMathématiques, Fasc. IX (1925). (Especially, Chapitre VII, Section II.) | JFM | Numdam

[Ca2]É. Cartan - Les groupes d'holonomie des espaces généralisés, Acta. Math. 48 (1926), 1-42. | JFM

[CMS] Q.-S. Chi, S. Merkulov, and L. Schwachhöfer - On the existence of infinite series of exotic holonomies. Inventiones Math. 126 (1996), 391-411. | Zbl | MR

[ChS] Q.-S. Chi and L. Schwachhöfer - Exotic holonomy on moduli spaces of rational curves, Differential Geom. App. 8 (1998), 105-134. | Zbl | MR

[Gr] M. Gromov - Carnot-Carathéodory spaces seen from within, in Sub-Riemannian geometry, Progr. Math. 144, Birkhäuser, Basel, 1996, 79-323. | Zbl | MR

[Jol] D. Joyce - Compact Riemannian 7 -manifolds with holonomy G 2 : I & II, J. Differential Geom. 43 (1996), 291-328, 329-375. | Zbl | MR

[Jo2] D. Joyce - Compact 8 -manifolds with holonomy Spin ( 7 ) , Inventiones Math. 123 (1996), 507-552. | Zbl | MR

[Jo3] D. Joyce - Compact manifolds with special holonomy, Oxford University Press, Oxford, 2000 (projected). | Zbl | MR

[KNa] S. Kobayashi and K. Nagano - On filtered Lie algebras and geometric structures, II, J. Math. Mech. 14 (1965), 513-521. | Zbl | MR

[KNo] S. Kobayashi and K. Nomizu - Foundations of Differential Geometry, Vols. 1 & 2, Wiley-Interscience, New York, 1963. | Zbl | MR

[LM] H. B. Lawson, Jr. and M. L. Michelsohn - Spin geometry, Princeton Math. Series 38, Princeton Univ. Press, Princeton, NJ, 1989. | Zbl | MR

[Me1] S. Merkulov - Moduli spaces of compact complex submanifolds of complex fibered manifolds, Math. Proc. Camb. Phil. Soc. 118 (1995), 71-91. | Zbl | MR

[Me2] S. Merkulov - Geometry of Kodaira moduli spaces, Proc. Amer. Math. Soc. 124 (1996), 1499-1506. | Zbl | MR

[Me3] S. Merkulov - Existence and geometry of Legendre moduli spaces, Math. Z. 226 (1997), 211-265. | Zbl | MR

[MS1] S. Merkulov and L. Schwachhöfer - Classification of irreducible holonomies of torsion-free affine connections, Ann. Math. (to appear). | Zbl | MR

[MS2] S. Merkulov and L. Schwachhöfer - Twistor solution of the holonomy problem, 395-402, The Geometric Universe, Science, Geometry and the work of Roger Penrose, S.A. Hugget (ed.), Oxford Univ. Press, 1998. | Zbl | MR

[PoS] Y. S. Poon and S. Salamon - Quaternionic Kähler 8 -manifolds with positive scalar curvature, J. Differential Geom. 33 (1991), 363-378. | Zbl | MR

[Sa] S. Salamon - Riemannian geometry and holonomy groups, Pitman Research Notes in Math., no. 201, Longman Scientific & Technical, Essex, 1989. | Zbl | MR

[Scho] J. Schouten - On the number of degrees of freedom of the geodetically moving systems, Proc. Kon. Acad. Wet. Amsterdam 21 (1918), 607-613.

[Schw] L. Schwachhöfer - On the classification of holonomy representations, Habilitationsschrift, Universität Leipzig, 1998.

[Wi] B. Wilking - On compact Riemannian manifolds with noncompact holonomy groups, 1999 preprint. URL: http://wwwmath.uni-muenster.de/math/inst/sfb/about/publ/wilking.ps | MR