TITLE

On the existence of nonlinear Dirac-geodesics on compact manifolds

AUTHOR(S)
Isobe, Takeshi
PUB. DATE
January 2012
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2012, Vol. 43 Issue 1/2, p83
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We show that for super-linear nonlinearity, there exists a 'non-trivial' nonlinear Dirac-geodesic on $${\mathbb{T}^n_{\Gamma}=\mathbb{R}^n/\Gamma}$$, a flat tori, in each 'bosonic' sector. We also show that for any compact Riemannian manifold with 'bumpy' metric, there exists a non-trivial nonlinear Dirac-geodesic in each bosonic sector if the nonlinearity is cubic or super-cubic and 'large'. Our proof is based on critical point theory, in particular, a generalized linking argument applied to a strongly indefinite functional on a fibered Hilbert manifold.
ACCESSION #
67363489

 

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