Edmond Bonan (born 27 January 1937 in Haifa, Mandatory Palestine) is a French mathematician, known particularly for his work on special holonomy. Although not a single example of G2 manifold or Spin(7) manifold had been discovered until thirty years later, Edmond Bonan nonetheless made a useful contribution by showing in 1966, that such manifolds would carry at least a parallel 4-form, and would necessarily be Ricci-flat,[1] propelling them as candidates for string theory.[2]
Biography
editAfter completing his undergraduate studies at the École polytechnique, Bonan went on to write his 1967 University of Paris doctoral dissertation in Differential geometry under the supervision of André Lichnerowicz.[3] From 1968 to 1997, he held the post of lecturer and then professor at the University of Picardie Jules Verne in Amiens, where he currently holds the title of professor emeritus. Early in his career, from 1969 to 1981, he also lectured at the École Polytechnique.
See also
editReferences
edit- ^ Bonan, Edmond (1966), "Sur les variétés riemanniennes à groupe d'holonomie G2 ou Spin(7)", Comptes Rendus de l'Académie des Sciences, 262: 127–129.
- ^ Publications of Edmond Bonan at the Comptes Rendus de l'Académie des Sciences de Paris – Séries I – Mathematics
- Structures presque quaternioniennes, vol. 258, 1964, pp. 792–795.
- Connexions presque quaternioniennes, vol. 258, 1964, pp. 1696–1699.
- Structures presque hermitiennes quaternioniennes, vol. 258, 1964, pp. 1988–1991.
- Tenseur de structure d'une variété presque quaternionienne, vol. 259, 1964, pp. 45–48.
- Structure presque quaternale sur une variété différentiable, vol. 261, 1965, pp. 5445–5448.
- Sur les variétés riemanniennes à groupe d'holonomie G2 ou Spin(7), vol. 320, 1966, pp. 127–129
- Sur un lemme adapté au théorème de Tietze-Uryshon, vol. 270, 1970, pp. 1226–1228.
- Relèvements-Prolongements à valeurs dans les espaces de Fréchet, vol. 272, 1971, pp. 714–717.
- Sur les relèvements-Prolongements à valeurs dans les espaces de Fréchet, vol. 274, 1972, pp. 448–450.
- Sur l'algèbre extérieure d'une variété presque hermitienne quaternionique, vol. 295, 1982, pp. 115–118.
- Sur l'algèbre extérieure d'une variété presque hermitienne quaternionique, vol. 296, 1983, pp. 601–602.
- Comparaison d'un corps convexe avec ses deux ellipsoïdes optimaux, vol. 315, 1992, pp. 557–560.
- Décomposition de l'algèbre extérieure d'une variété hyperkählérienne, vol. 320, 1995, pp. 457–462.
- Sur certaines variétés presque hermitiennes quaternioniques, vol. 320, 1995, pp. 981–984.
- Sur certaines variétés presque hyperhermitiennes, vol. 321, 1995, pp. 95–96.
- Bonan, Edmond (2006), "Connexions pour les variétés riemanniennes avec une structure de type G2 ou Spin(7)", Comptes Rendus Mathématique, 343 (11–12): 755–758, doi:10.1016/j.crma.2006.10.019
- Kraines, Vivian Yoh (1966), "Topology of quaternionic manifolds", Trans. Am. Math. Soc., 122 (2): 357–367, doi:10.1090/s0002-9947-1966-0192513-x.
- Dmitri V. Alekseevsky (1968), "Riemannian spaces with non-standard holonomy groups, Funct. Anal. and its Applications", Funct. Anal. Appl., 308 n°2: 1–10.
- S. Marchiafava (1970), "Sulle variet a a struttura quaternionale generalizzata", Rend. Mat., 3: 529–545.
- S.Marchiafava; G.Romani (1976), "Sui fibrati con struttura quaternionale generalizzata", Annali di Matematica Pura ed Applicata, 107: 131–157, doi:10.1007/bf02416470, S2CID 121638815.
- V. Oproiu (1977), "Almost quaternal structures", An. St. Univ. Iazi, 23: 287–298.
- M. Fernandez; A. Gray (1982), "Riemannian manifolds with structure group G2", Ann. Mat. Pura Appl., 32: 19–845, doi:10.1007/BF01760975, S2CID 123137620.
- Salamon, Simon (1982). "Quaternionic Kähler manifolds". Invent. Math. 67: 143–171. Bibcode:1982InMat..67..143S. doi:10.1007/bf01393378. S2CID 118575943.
- T.Nagano; M.Takeuchi (1983), "Signature of quaternionic Kaehler manifolds", Proc. Japan Acad., 59 (8): 384–386, doi:10.3792/pjaa.59.384.
- V. Oproiu (1984), "Integrability of almost quaternal structures", An. St. Univ."Al. I.Cuza" Iasi, 30: 75–84.
- M.Fernandez (1986), "A classification of Riemannian with structure Spin(7)", Annali di Matematica Pura ed Applicata, Series 4, 143: 101–122, doi:10.1007/bf01769211, S2CID 123192881.
- Bryant, Robert L.; Salamon, Simon M. (1989), "On the construction of some complete metrics with exceptional holonomy", Duke Math. J., 58 (3): 829–850, doi:10.1215/s0012-7094-89-05839-0.
- Swann, Andrew (1989), "Aspects symplectiques de la Géométrie quaternionique", Comptes Rendus de l'Académie des Sciences, Série I, 308: 115–118.
- Swann, Andrew.F. (1990), HyperKähler and Quaternionic Kähler Geometry (PDF).
- Edmond Bonan, Isomorphismes sur une variété presque hermitienne quaternionique, Proc. of the Meeting on Quaternionique Structures in Math.and Physics SISSA, Trieste, (1994), 1-6.
- Dmitri V. Alekseevsky; E.Bonan; S.Marchiafava (1995), "On some structure equations for almost quaternionic Hermitian manifolds", Complex Structures and Vector Fields: 114–135.
- Dominic Joyce, Compact manifolds with special holonomy, Oxford Mathematical Monographs. Oxford University Press, Oxford, 2000.
- André Lichnerowicz, Alain Connes, and Marco Schutzenberger, Triangle of Thoughts, American Mathematical Society, 2000.
- Karigiannis, Spiro, "Flows of G2 and Spin(7) structures" (PDF), Mathematical Institute, University of Oxford.
- Bonan, Edmond (1986), "Sur les sélections injectives du type fini", Cahiers de Topologie et Géométrie Différentielle Catégoriques, 27 (2): 147–150
- ^ Bonan, Edmond (1967), "Sur les G-structures de type quaternionien", Cahiers de Topologie et Géométrie Différentielle Catégoriques, 9 (4): 389–463