Dirac Operators in Riemannian Geometry

Spinorially Twisted Spin Structures, III: CR Structures

“…In this section, we briefly recall basic facts about Clifford algebras, the Spin group and the standard Spin representation [10]. We also define the twisted Spin groups and representations, the antisymmetric 2-forms and endomorphisms associated to a twisted spinor, recall the definition of twisted partially pure spinor, and describe the isotropy representations of certain homogeneous spaces that will furnish examples later on.…”

“…Cartan in 1913. We refer the reader to Hitchin's seminal paper [13], Friedrich's textbook [10], as well as to [22,15] for the more recent development of Seiberg-Witten theory and its notorious results on 4-manifold geometry and topology.…”

Dirac-harmonic maps from degenerating spin surfaces I: the Neveu–Schwarz case

“…For simplicity of notation, we denote ∇ M by ∇. The Dirac operator / ∂ is locally given by / ∂ψ := e 1 ·∇ e 1 ψ + e 2 ·∇ e 2 ψ for a local orthonormal frame {e 1 , e 2 } of T M and ψ ∈ M. We refer to [9,10,13] for more background material on spin structures and Dirac operators and to [11] …”

A structure theorem of Dirac-harmonic maps between spheres

“…We refer to [4][5][6] for more background material on spin structures and Dirac operators and to [7,8] for more background material on harmonic maps.…”

“…hence λ(z(z))|z| −4 is regular atz = 0; then there exists a constant c > 0, such that lim z→∞ λ(z)|z| 4 and there exist two meromorphic function u 1 , u 2 on C * such that Let u 1 be a function on C * (possibly with isolated singularities) such that…”