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Surfaces in 𝕊 3 and 3 via spinors

Bertrand Morel (2004/2005)

Séminaire de théorie spectrale et géométrie

We generalize the spinorial characterization of isometric immersions of surfaces in 3 given by T. Friedrich to surfaces in 𝕊 3 and 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.

Surfaces kählériennes de volume fini et équations de Seiberg-Witten

Yann Rollin (2002)

Bulletin de la Société Mathématique de France

Soit M = ( ) une surface complexe réglée. Nous introduisons des métriques de volume fini sur M dons les singularités sont paramétrisées par une structure parabolique sur le fibré . Nous généralisons alors un résultat de Burns-deBartolomeis et Le Brun, en montrant que l’existence de métriques kählériennes singulières, de volume fini, à courbure scalaire constante négative ou nulle sur M est équivalente à une condition de polystabilité parabolique sur  ; de plus ces métriques proviennent toutes de quotients...

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