Mathematics – Differential Geometry
Scientific paper
2003-05-09
C. R. Math. Acad. Sci. Paris 338 (2004), 561-564
Mathematics
Differential Geometry
Scientific paper
10.1016/j.crma.2004.01.030
We prove that on a compact $n$-dimensional spin manifold admitting a non-trivial harmonic 1-form of constant length, every eigenvalue $\lambda$ of the Dirac operator satisfies the inequality $\lambda^2 \geq \frac{n-1}{4(n-2)}\inf_M Scal$. In the limiting case the universal cover of the manifold is isometric to $R\times N$ where $N$ is a manifold admitting Killing spinors.
Moroianu Andrei
Ornea Liviu
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