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Given a Riemannian space with non-integrable structure we find a characteristic connection,
which is adapted to the geometry and whose torsion is a three-form. Assuming the existence
of a spin structure there is a 1-parameter family of Dirac type operators
associated to the underlying geometry including Kostant´s cubic Dirac operator
and the Dolbeault operator in special cases. Now, interesting problems concern
- optimal eigenvalue estimates
- existence of solutions of derived spinorial field equations
- construction of new examples of compact spaces with special geometry
Currently, I am member of the Global Analysis group at the mathematical institute of University Bonn.
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