Spinor analysis on C<sup>2</sup> and on conformally flat 4-manifolds

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  • KORI Tosiaki
    DEPARTMENT OF MATHEMATICS SCHOOL OF SCIENCE AND ENGINEERING UNIVERSITY OF WASEDA

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  • Spinor analysis on C2 and on conformally flat 4-manifolds

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Abstract

Abstract. The present paper is concerned with extensions of complex analysis on the complex plane C to conformally flat 4-manifolds. We shall give in an explicit form a fundamental system of spinors that will serve as the basis vectors for the Laurent expansion. Restricted to a sphere around the center of the expansion these spinors form a complete orthonormal system of eigenspinors of the tangential Dirac operator on the sphere, and give a basis of the representations of Spin (4). We shall also give the definition of meromorphic spinors and residues, and prove under some hypothesis that, on a compact conformally flat 4-manifold, the sum of the residues of a meromorphic spinor is zero.

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