리만 다양체의 홀로노미군

  • 김홍종 (서울대학교 수리과학부)
  • Published : 2000.10.01

Abstract

Holonomy groups of Riemannian manifolds are surveyed.

Keywords

References

  1. Lectures on Exceptional Lie Groups J. Adams
  2. Functional Anal. Appl. v.2 Riemannian spaces with exceptional holonomy groups D. Alekseevski
  3. Trans. Amer. Math. Soc v.79 A theorem 9on holonomy W. Ambrose;I. M. Singer
  4. Lec. Notes in Math. v.1422 HyperKahler manifolds;Complex Geometry and Analysis M. Atiyah;Ed. V. Villani(ed.)
  5. J. Diff. Geom v.18 Varietes Kahleriennes dont la lere classes de Chern est nulle A. Beauville
  6. Mull. Soc. Math v.83 Sur les groupes d'holonomie des varietes a connexion affine et des varietes riemanniennes M. Berger
  7. Amer. Math. Soc. Riemannian Geometry During the Second Half of the Twentieth Century M. Berger
  8. Notices of the Qmer. Math. Soc v.47 Encounter with a Geometer M. Berger
  9. Einstein Manifolds A. L. Besse
  10. Bull. Amer. Math. Soc. v.55 Some remarks about lie groups transitive on spheres and tori A. Borel
  11. C. R. Acad. Sci. Paris v.230 Le plan projectif des octaves et les spheres comme espaces homogenes A. Borel
  12. C. R. Acad. Sci. Paris v.234 Groups d'holonomie des varietes riemanniennes A. Borel;A. Lichnerowicz
  13. Seminaire Bourbaki v.710 Premieres Formes de Chern des varietes Kahlereinnes compactes J. Bourguignon
  14. Global differential geometry and global analysis(Berlin, 1979) v.838 Ricci curvature and Einstein metrics J. Bourguignon
  15. J. Diff. Geom. v.17 Submanifolds and special structrues on the octonians R. Bryant
  16. Ann. Math. v.126 Metrics with exceptional holonomy R. Bryant
  17. Classical, Exceptional and exotic Holonomies;A Status Report v.1 Semin. Congr R. Bryant
  18. Seminaire BOURBAKI no.861 Recent Advances in the theory of holonomy R. Bryant
  19. Duke Math. J. v.58 On the construction of some complete metrics with exceptional holonomy R. Bryant;S. Salamon
  20. On Kahler manifolds with vanishing canonical class in Algebraic Geometry and Topology E. Calavi
  21. Ann. Eco. Norm. Sup. v.12 Metriques Kahleriennes et fibres holomorphes E. Calavi
  22. Ann. Sci. Ecole Norm. Sup. v.40;41;42 Sur les varietes a connexion affine et la theorie de la relativite generalisee E. Cartan
  23. Acta. Math. v.48 Les groupes d'holonomie des espaces generalises E. Cartan
  24. Exploring Curvature J. Casey
  25. Commen. Math. Helv. v.26 Sur la reductibilite d'un espace de riemann G. de Rham
  26. Les connexion infiniteestimalesdans un espace fibre defferentiable C. Ehresmann
  27. Zeitschrift fur mathematik und physik v.62 Entwurf einer verallgemeinerten Relativitatstheorie und einer Theorie des Gravitation;Ⅰ.Physikalische Teil von A. Einstein,Ⅱ. Mathematischer Teil von M. Grossmann A. Einstein;m. Grossmann
  28. Ann. Mat. Pura. Appl. v.143 A Classification of Riemannian Manifolds with structure Group Spin(7) M. Fernandez
  29. Comm. Math. Phys. v.203 no.1 Special Kahler maniflods A. Freed
  30. Progress in Math. v.38 On primitively symplectic compact Kahler V-manifolds of dimension four A. Fujiki;Ueno(ed.)
  31. Representation Theory W. Fulton;J. Harris
  32. Rend Sem. Mat. Fis. Milano v.61 Sign and geometric meaning of curvature M. Gromov
  33. Acta. Mathematica v.148 Calibrated Geometries R. Harvey;H. Lawson
  34. Differential Geometry, Lie Groups, and Symmetric Spaces S. Helgason
  35. Riemannian Geometry and Geometric Analysis J. Jost
  36. J. Diff. Geom. v.43 Compact Riemannian 7-manifolds with holonomy G₂ Ⅰ,Ⅱ D. D. Joyce
  37. Invent. Math. v.123 Compact 8-manifolds with holonomy Spin(7) D. D. Joyce
  38. Lecture Notes in pure and Appl. Math v.184 Compact Manifolds with exceptional holonomy, Geometry and Physics(Aarhus,1995) D. D. Joyce
  39. Doc. Math. Extra Vol. ICM 1998 Ⅱ Compact Manifolds with exceptional Holonomy D. D. Joyce
  40. A new construction of compact 8-manifolds with holonomy Spin(7) D. D. Joyce
  41. Compact manifolds with special holonomy D. D. Joyce
  42. Foundations of Differential Geomety, Ⅰ,Ⅱ S. Kobayashi;K. Nomizu
  43. Theorie globale des connexions et des groupes d'holonomie A. Lichnerowicz;Cremonese(ed.)
  44. Geometry Fron a Differentiable Viewpoint J. McCleary
  45. Ann. of Math.(2) v.150 no.3 Classificationof irreducible holonomies of torsion-free affine connection S. A. Merkulov;L. J. Schwachhofer
  46. Ann. Math. v.44 Transformation groups of spheres D. Montgomery;H. Samelson
  47. Invent. Math. v.77 Symplectic structure on the module sapce of sheaves on an abelian of K3 surfaces S. Mukai
  48. Tensor Analysis E. Nelson
  49. Ann. Math. v.65 Complex analytic coordinates in almost complex manifolds A. Newlander;l. Nirenberg
  50. Proc. Amer. Math. Soc. v.12 The existence of complete Riemannian metrics K. Nomixu;H. Ozeki
  51. Amer. Math. Monthly v.102 Geometry and Foucault pendulum J. Oprea
  52. Amer. Math. Soc Mathematical physics on the 20th and 21st century;in Mathematics Frontiers and Perspectives R. Penrose;V. Arnold(ed.);M. Atiyah(ed.);P. Lax(ed.);B. Mazur(ed.)
  53. Riemanniam Geometry P. Petersen
  54. Bull. Amer. Math. Soc. v.36 Aspects of global Riemannian geometry P. Petersen
  55. The Mathematical Intelligencer v.21 no.2 Yea Why Try Her Raw Wet Hat;A Tour of the Smallest Projective Space B. Ploster
  56. Differential Geometric Structures W. Poor
  57. Amer. Math. Soc. v.149 Riemannian Geometry;Translations of Mathematical Monographs 149 T. Sakai
  58. Riemannian geometry and holonomy groups S. Salamon
  59. Ann. Math. v.76 On the transitivity of holonomy system J. Simons
  60. A Comprehensine Introduction to DIFFERENTIAL GEOMETRY v.Ⅱ M. Spivak
  61. Math. Res. Lett. v.6 no.5;6 New examples of compact 8-manifolds of holonomy Spin(7) C. Taylor
  62. Introduction to Geometry of Manifolds with Symmetry V.V. Trofimov
  63. On compact Riemannian Manifolds with noncompact holonomy groups B. Wilking
  64. Amer. Math. Soc. v.Ⅴ Mahic, mystery, and matrix, in Mathematics;Frontiers and Perspectives E. Witten;b. Arnold(ed.);M. Atiyag(ed.);P. Lax(ed.);B. Mazur(ed.)
  65. Spaces of constant curbature J. A. Wolf
  66. Proc. Natl. Acad. Sci. USA v.74 Calabi's conjecture and some new results in algebraic geometry S. T. Yau
  67. Com. Pure and Appl. Math. v.31 On the Ricci curvature of a compact Kahler manifold and the compex monge-Ampere equation I S. T. Yau