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Nearly Kähler and nearly parallel G 2 -structures on spheres

Thomas Friedrich (2006)

Archivum Mathematicum

In some other context, the question was raised how many nearly Kähler structures exist on the sphere 𝕊 6 equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue λ = 12 of the Laplacian acting on 2 -forms. A similar result concerning nearly parallel G 2 -structures on the round sphere 𝕊 7 holds, too. An alternative proof by Riemannian Killing spinors is also indicated.

Non-topological condensates in self-dual Chern-Simons gauge theory

Takashi Suzuki, Futoshi Takahashi (2004)

Banach Center Publications

This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.

On a problem of Seiberg and Witten

David E. Barrett (1998)

Annales Polonici Mathematici

We describe alternate methods of solution for a model arising in the work of Seiberg and Witten on N = 2 supersymmetric Yang-Mills theory and provide a complete argument for the characterization put forth by Argyres, Faraggi, and Shapere of the curve I m a D / a = 0 .

On multivortex solutions in Chern-Simons gauge theory

Michael Struwe, Gabriella Tarantello (1998)

Bollettino dell'Unione Matematica Italiana

Motivati dall'analisi asintotica dei vortici nella teoria di Chern-Simons-Higgs, si studia l'equazione - Δ u = λ e u Ω e u d x - 1 Ω , u H 1 Ω dove Ω = R 2 / Z 2 é il toro piatto bidimensionale. In contrasto con l'analogo problema di Dirichlet, si dimostra che per λ 8 π , 4 π 2 l'equazione ammette una soluzione non banale. Tale soluzione cattura il carattere bidimensionale dell'equazione, nel senso che, per tali valori di λ , l'equazione non può ammettere soluzioni (periodiche) non banali dipendenti da una sola variabile (vedi [10]).

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