Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toda frames, harmonic maps and extended Dynkin diagrams   We prove that all immersions of a genus one surface into G/T possessing a
Toda frame can be constructed by integrating a pair of commuting vector fields
on a finite dimensional Lie algebra. Here G is any simple real Lie group (not
necessarily compact), T is a Cartan subgroup and the k-symmetric space
structure on G/T is induced from the Coxeter automorphism. We provide necessary
and sufficient conditions for the existence of a Toda frame for a harmonic map
into G/T and describe those G/T to which the theory applies in terms of
involutions of extended Dynkin diagrams.

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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th