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Edmond Bonan (born January 27, 1937, Haifa) is a French mathematician, known particularly for his work on special holonomy

$$\sum_{0\leq i\leq n }\ \sum_{ 0\leq j\leq i }\ \sum_{{1\over 2}(j-i)\leq k\leq n-i }\ \sum_{0\leq g\leq n-i-k_+}\ \sum_{ 0\leq h \leq i-j-2k_-}K_1^hK_0^g\zeta_{i,j,i-j+2k}$$

In fact Edmond Bonan proved that on a compacte hyperkähler manifold


 * $$ p\leq n, \ b_{2p}\geq (p+1)(p+2)/2$$



p\leq n-1, \ b_{2p-1}\equiv 0, \ mod \ 4 $$


 * $$p\leq n, \ \phi_p=\sum_{ 0\leq a+b+c\leq [p/2]}F_i^a\wedge F_j^b\wedge F_k^c\wedge \psi_{a,b,c},\   \    F_i\wedge*\psi_{a,b,c}= F_j\wedge*\psi_{a,b,c}= F_k\wedge*\psi_{a,b,c}=0

$$

$$\sum_{0\leq i\leq n }\ \sum_{ 0\leq j\leq i }\ \sum_{{1\over 2}(j-i)\leq k\leq n-i }\ \sum_{0\leq g\leq n-i-k_+}\ \sum_{ 0\leq h \leq i-j-2k_-}K_1^hK_0^g\zeta_{i,j,i-j+2k}$$

In fact Edmond Bonan proved that on a compacte hyperkähler manifold



p\leq n, \ b_{2p}\geq (p+1)(p+2)/2$$



p\leq n-1, \ b_{2p-1}\equiv 0, \ mod \ 4 $$

Publications of Edmond Bonan at the Comptes Rendus de l'Académie des Sciences Paris - Séries I - Mathematics .
 * Simon Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), 143-171.
 * 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.
 * 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.
 * Simon Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), 143-171.
 * 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.
 * 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.
 * 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.
 * 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.
 * 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.
 * 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.
 * André Lichnerowicz, Alain Connes, and Marco Schutzenberger, Triangle of Thoughts, American Mathematical Society, 2000.

Biography
Alumnus of the École polytechnique, Bonan completed in 1967 his doctoral dissertation in Differential geometry at the University of Paris under the supervision of  André Lichnerowicz. From 1968 to 1997, he held the post of lecturer and then professor at the University of Picardie Jules Verne in Amiens, currently professor emeritus. At the same time, from 1969 to 1981, he lectured at École polytechnique.