Harmonic spinors on Riemann surfaces. (English) Zbl 0840.53015

Bureš, Jarolím

Bureš, J. (ed.) et al., Proceedings of the winter school on geometry and physics, Zdíkov, Czech Republic, January 1993. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 37, 15-32 (1994).

The author describes the spin geometry and Dirac operators on real and complex manifolds. He starts with the case of real manifolds. He reviews the basic notion of spin geometry, including the \(\text{spin}^c\) structure, in the language of bundle theory and Clifford algebras. On Kähler manifolds it leads to the fact that the spin structures are in one-to-one correspondence with the holomorphic line bundles which are square-roots of the canonical line bundle of the manifold. Then he specializes to the Riemann surfaces, where the expressions of the previous notions are more explicitly given, e.g. the relation between the spin structures and the \(\theta\)-characteristics are discussed.
For the entire collection see [Zbl 0823.00015].

Reviewer: I-Hsun Tsai (Taipei)

MSC:

53C27	Spin and Spin\({}^c\) geometry
30F15	Harmonic functions on Riemann surfaces
53C55	Global differential geometry of Hermitian and Kählerian manifolds
15A66	Clifford algebras, spinors

Keywords:

Dirac operators; Clifford algebra; spin structures