Global Analysis of Manifolds and Conformal Structures

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The purposes of this research project was to accomplish synthetic investigation for geometry of manifolds, mainly for conformal structures and to obtain progressive reserach results.By considering the last year's research progress situation we held in August, 1997 the geometry symposium, greatly organized, on a nationwide scale (participants 251, survey lectures 3, ordinary talks 53). In this symposium we could get exchanging of informations among researchers and intension and broadening of researches related to the purposes. As its consequences, for the research of global analysis on conformal structures M.Itoh, myself, the chief researcher, together with coresearchers, K.Akutagawa, S.Nayatani, Y.Izeki, S.Kato were able to obtain plenty of researches on the whole conformal geometry covering self-dual 4-manifolds, conformally flat manifolds and Einstein-Weyl manifolds.In the other areas, that is, geometry of vector bundles, gauge fields great contributions were done by this project, especially in the field of self-dual bundles on quaternionic Kaehler manifolds. And also investigations done by this project took a progressive step in the direction of (almost) Kaehler structures. Furthermore, homogeneous manifolds, Rie-mannian geometry, symplectic geometry, geometry of curves and surfaces could get research progresses.