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Title: Affine harmonic maps
Authors: Jost J.
Şimşir, Fatma Muazzez
Keywords: Affine flat connection
affine harmonic map
dually flat
Issue Date: 2009
Abstract: We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemannian geometry of the target. These maps are called affine harmonic. We show an existence result for affine harmonic maps in a given homotopy class when the target has nonpositive sectional curvature and some global nontriviality condition is met. An example shows that such a condition is necessary. The analytical part is made difficult by the absence of a variational structure underlying affine harmonic maps. We therefore need to combine estimation techniques from geometric analysis and PDE theory with global geometric considerations. © 2009, by Oldenbourg Wissenschaftsverlag, Leipzig, Germany. All rights reserved.
ISSN: 0174-4747
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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