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Displaying similar documents to “Dirac operators on hypersurfaces”

On the conformal relation between twistors and Killing spinors

Friedrich, Thomas

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[For the entire collection see Zbl 0699.00032.] The author considers the conformal relation between twistors and spinors on a Riemannian spin manifold of dimension n ≥ 3 . A first integral is constructed for a twistor spinor and various geometric properties of the spin manifold are deduced. The notions of a conformal deformation and a Killing spinor are considered and such a deformation of a twistor spinor into a Killing spinor and conditions for the equivalence of these quantities is indicated. ...

Surfaces in 𝕊 3 and ℍ 3 via spinors

Bertrand Morel (2004-2005)

Séminaire de théorie spectrale et géométrie

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We generalize the spinorial characterization of isometric immersions of surfaces in ℝ 3 given by T. Friedrich to surfaces in 𝕊 3 and ℍ 3 . The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also holds in the case of hypersurfaces in the Euclidean 4 -space.

The positive mass theorem for ALE manifolds

Mattias Dahl (1997)

Banach Center Publications

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We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.