Examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of . Dirac Operators in Riemannian Geometry (Graduate Studies in Mathematics) Read more. Dirac Operators and Spectral Geometry. Read more. Dirac Operators and Spectral Geometry. Read more. Dirac operators and spectral geometry. Read more. Dirac operators and spectral geometry. Theorem: The dimension of the kernel of the Dirac operator is a conformal invariant. Corollary: Let (Mn,g) be a compact Riemannian spin manifold. If the metric is conformally equivalent to a metric g. 1 with positive scalar curvature, then the kernel of the Dirac operator is trivial.

# Dirac operators in riemannian geometry pdf

Riemannian Geometry -- EP.5 (Differentiable Manifolds), time: 7:33

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