Research for the twistor theory concerning families of holomorphic disks and geometry of indefinite metrics

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New general theories, reduction theories and many examples are established in the field of the theory of twistor correspondence concerning with families of holomorphic disks. We obtained new results on the theories of hyperbolic PDEs and integral transforms, and we found unknown relations between twistor theory and these theories. Such relations give new insights to the theory of indefinite geometries. The results in this research give a new way to develop indefinite geometries.