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Harmonic morphisms from the classical compact semisimple Lie groups

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Sigmundur Gudmundsson, Anna Sakovich

Differential Geometry · Submitted 19 Nov 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups SL(n,R), SU(2n), Sp(n,R), SO(2n), SO(p,q), SU(p,q) and Sp(p,q) equipped with their standard dual semi-Riemannian metrics.

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arXiv IDmath/0611574 (version 3)
Pith IDTKUFJG7H, Pith's permanent record of this paper and its review
CitationAnna Sakovich, Sigmundur Gudmundsson. "Harmonic morphisms from the classical compact semisimple Lie groups." arXiv:math/0611574 (2006). https://pith.science/paper/TKUFJG7H
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,054 input tokens.

What the abstract itself states, as probabilities: claims first 0.80 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.44 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

In this paper we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups SL(n,R), SU(2n), Sp(n,R), SO(2n), SO(p,q), SU(p,q) and Sp(p,q) equipped with their standard dual semi-Riemannian metrics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. contribution 0.80 0.94 0.16 asserted 1.00
s1 This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. result 0.65 0.93 0.16 asserted 1.00
s2 We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups SL(n,R), SU(2n), Sp(n,R), SO(2n), SO(p,q), SU(p,q) and Sp(p,q) equipped with their standard dual semi-Riemannian metrics. contribution 0.84 0.95 0.41 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups SL(n,R), SU(2n), Sp(n,R), SO(2n), SO(p,q), SU(p,q) and Sp(p,q) equipped with their standard dual semi-Riemannian metrics.

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