20.02.2025, 10:15
– Raum 0.12 in Haus 9
Forschungsseminar Differentialgeometrie
Kähler and quaternion-Kähler manifolds of non-negative curvature
Uwe Semmelmann (Stuttgart)
Peter Grabs
We investigate the Rarita-Schwinger operator using methods previously applied in the Dirac case. The structure of the underlying manifold \(\mathcal{S}^3 \cong \mathrm{SU}(2)\) as a Lie group implies that all associated bundles are trivial, so their sections can be seen as ordinary functions.
Due to the compactness of \(\mathcal{S}^3\), the Peter-Weyl theorem provides a decomposition of such function spaces into finite-dimensional summands. This simplifies the analysis of the operator, reducing the problem to a finite-dimensional setting where eigenvalues can be computed using linear algebra techniques.