Quaternionic structures in mathematics and physics : proceedings of the second meeting ; Rome, Italy, 6-10 September, 1999

Since 1994, after the first meeting on "Quaternionic Structures in Mathematics and Physics", interest in quaternionic geometry and its applications has continued to increase. Progress has been made in constructing new classes of manifolds with quaternionic structures (quaternionic Kaehler, hyper Kaehler, hyper-complex, etc), studying the differential geometry of special classes of such manifolds and their submanifolds, understanding relations between the quaternionic structure and other differential-geometric structures, and also in physical applications of quaternionic geometry. Some generalizations of classical quaternion-like structures (like HKT structures and hyper-Kaehler manifolds with singularities) appeared naturally and were studied. Some of those results are published in this book. This book should be of interest to researchers and graduate students in geometry, topology, mathematical physics and theoretical physics. Hypercomplex structures on special classes of nilpotent and solvable Lie groups / M.L. Barberis -- Twistor quotients of hyperKahler manifolds / R. Bielawski -- Quaternionic contact structures / O. Biquard -- A new construction of homogeneous quaternionic manifolds and related geometric structures / V. Cortes -- Spencer manifolds / St. Dimiev, R. Lazov and N. Milev -- Quaternion Kahler flat manifolds / I.G. Dotti -- Hyperholomorphic functions in R4 / S.-L. Eriksson-Bique -- A note on the reduction of Sasakian manifolds / G. Grantcharov and L. Ornea -- A theory of quaternionic algebra, with applications to hypercomplex geometry / D. Joyce -- A canonical Hyperkahler metric on the total space of a cotangent bundle / D. Kaledin -- Equivariant cohomology rings of toric HyperKahler manifolds / H. Konno -- An introduction to pseudotwistors basic constructions / J. Lawrynowicz and O. Suzuki -- Differential geometry of circles in a complex projective space / S. Maeda and T. Adachi -- On special 4-planar mappings of almost hermitian quaternionic spaces / J. Mikes, J. Belohlavkova and O. Pokorna -- Special spinors and contact geometry / A. Moroianu -- Generalized ADHM-construction on Wolf spaces / Y. Nagatomo -- Sp(1)n-invariant quaternionic Kahler metric / T. Nitta and T. Taniguchi -- Brane solitons and hypercomplex structures / G. Papadopoulos -- Hypercomplex geometry / H. Pedersen -- Examplex of hyper-Kahler connections with torsion / Y.S. Poon -- Theorems of existence of local and global solutions of PDEs in the category of noncommutative quaternionic manifolds / A. Prastaro -- Optimal control problems on the Lie group SP(1) / M. Puta -- A new weight system on chord diagrams via hyperKahler geometry / J. Sawon -- Quaternionic group representations and their classifications / G. Scolarici and L. Solombrino -- Vanishing theorems for quaternionic Kahler manifolds / U. Semmelmann and G. Weingart -- Weakening holonomy / A. Swann -- Maxwell's vision: Electromagnetism with Hamilton's quaternions / D. Sweetser and G. Sandri -- Special Kahler geometry / A. Van Proeyen -- Singularities in hyperKahler geometry / M. Verbitsky During the last five years, after the first meeting on “Quaternionic Structures in Mathematics and Physics”, interest in quaternionic geometry and its applications has continued to increase. Progress has been made in constructing new classes of manifolds with quaternionic structures (quaternionic Kähler, hyper-Kähler, hyper-complex, etc.), studying the differential geometry of special classes of such manifolds and their submanifolds, understanding relations between the quaternionic structure and other differential-geometric structures, and also in physical applications of quaternionic geometry. Some generalizations of classical quaternion-like structures (like HKT structures and hyper-Kähler manifolds with singularities) appeared naturally and were studied. Some of those results are published in this book. During the last five years, after the first meeting on "Quaternionic Structures in Mathematics and Physics", interest in quaternionic geometry and its applications has continued to increase. Progress has been made in constructing new classes of manifolds with quaternionic structures (quaternionic Kahler, hyper-Kahler, hyper-complex, etc.), studying the differential geometry of special classes of such manifolds and their submanifolds, understanding relations between the quaternionic structure and other differential-geometric structures, and also in physical applications of quaternionic geometry. Some generalizations of classical quaternion-like structures (like HKT structures and hyper-Kahler manifolds with singularities) appeared naturally and were studied. Some of those results are published in this book