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Minimal and Conformal Foliations of Codimension two on Riemannian Lie Groups

Turner, Thomas LU (2020) In Master's Theses in Mathematical Sciences MATM01 20201
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Abstract
This thesis is an investigation into the construction of foliations that admit locally defined harmonic morphisms into the complex plane i.e. minimal horizontally conformal foliations of codimension two. The primary aim of this thesis is to test a conjecture posed by Sigmundur Gudmundsson regarding the compactness and semisimplicity of the subgroup generating the foliation. We provide experimental results using the compact semisimple Lie group $\SU2$ and its non-compact companion $\SLR2$ that seemingly confirm the main aspects of the conjecture. We provide further results in accordance with the conjecture when the subgroup generating the foliation is not semisimple.
Please use this url to cite or link to this publication:
author
Turner, Thomas LU
supervisor
organization
course
MATM01 20201
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Riemannian Geometry, Lie Groups, Harmonic Morphisms
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3116-2020
ISSN
1404-6342
other publication id
2020:E26
language
English
id
9016369
alternative location
http://www.matematik.lu.se/matematiklu/personal/sigma/students/Thomas-Turner-MSc.pdf
date added to LUP
2024-10-07 13:53:03
date last changed
2024-10-07 14:02:01
@misc{9016369,
  abstract     = {{This thesis is an investigation into the construction of foliations that admit locally defined harmonic morphisms into the complex plane i.e. minimal horizontally conformal foliations of codimension two. The primary aim of this thesis is to test a conjecture posed by Sigmundur Gudmundsson regarding the compactness and semisimplicity of the subgroup generating the foliation. We provide experimental results using the compact semisimple Lie group $\SU2$ and its non-compact companion $\SLR2$ that seemingly confirm the main aspects of the conjecture. We provide further results in accordance with the conjecture when the subgroup generating the foliation is not semisimple.}},
  author       = {{Turner, Thomas}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Minimal and Conformal Foliations of Codimension two on Riemannian Lie Groups}},
  year         = {{2020}},
}