## Connections on naturally reductive spaces and their Dirac operators. (Connexions sur les espaces homogènes naturellement réductifs et leurs opérateurs de Dirac.)(French)Zbl 1010.53024

In a homogeneous space whose metric is naturally reductive a set of connections is regarded, depending on a parameter $$t$$. The author proves that the Dirac operator for a certain value of $$t$$ coincides with the so-called cubic Dirac operator introduced by B. Kostant in 1999. Further, an eigenvalue estimate for the first eigenvalue of this operator is provided as well as some applications to string theory.
Reviewer: Johann Lang (Graz)

### MSC:

 53C05 Connections (general theory) 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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### References:

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