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Complete Minimal Submanifolds of Classical Non-Compact Riemannian Symmetric Spaces

Larsen, Lucas LU (2025) In Master’s Theses in Mathematical Sciences MATM03 20251
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract (Swedish)
In this thesis we employ the method of eigenfamilies in order to construct explicit examples of complete minimal submanifolds in the classical non-compact Riemannian symmetric spaces
$$\SLR n/\SO(n),\ \Sp(n,\R)/\UU(n),\ \SO^*(2n)/\UU(n),\ \SU^*(2n)/\Sp(n).$$
In each case, we produce a multidimensional parametrized family of complete minimal submanifolds of codimension two. The results form a continuation of the work in \cite{Geg-Gud-1}, which concerns the classical compact symmetric spaces.

The approach is largely elementary, accessible to readers with a basic background in differential geometry and Lie groups. Chapters \ref{ch:eigen} and \ref{ch:symmetric} serve as an introduction to the theory of eigenfunctions and Riemannian... (More)
In this thesis we employ the method of eigenfamilies in order to construct explicit examples of complete minimal submanifolds in the classical non-compact Riemannian symmetric spaces
$$\SLR n/\SO(n),\ \Sp(n,\R)/\UU(n),\ \SO^*(2n)/\UU(n),\ \SU^*(2n)/\Sp(n).$$
In each case, we produce a multidimensional parametrized family of complete minimal submanifolds of codimension two. The results form a continuation of the work in \cite{Geg-Gud-1}, which concerns the classical compact symmetric spaces.

The approach is largely elementary, accessible to readers with a basic background in differential geometry and Lie groups. Chapters \ref{ch:eigen} and \ref{ch:symmetric} serve as an introduction to the theory of eigenfunctions and Riemannian symmetric spaces, respectively. In Chapter \ref{ch:matrix} we establish some useful notation and definitions for working with matrix Lie groups. Finally, each of the Chapters \ref{ch:slr}, \ref{ch:spr}, \ref{ch:sox} and \ref{ch:sux} are dedicated to one of the symmetric spaces in question. (Less)
Please use this url to cite or link to this publication:
author
Larsen, Lucas LU
supervisor
organization
course
MATM03 20251
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Riemannian symmetric space, eigenfunction, minimal submanifold, Lie group
publication/series
Master’s Theses in Mathematical Sciences
report number
LUNFMA-3159-2025
ISSN
1404-6342
other publication id
2025:E92
language
English
id
9210406
alternative location
https://www.matematik.lu.se/matematiklu/personal/sigma/students/Lucas-Larsen-MSc.pdf
date added to LUP
2025-09-01 13:37:05
date last changed
2025-09-01 13:37:05
@misc{9210406,
  abstract     = {{In this thesis we employ the method of eigenfamilies in order to construct explicit examples of complete minimal submanifolds in the classical non-compact Riemannian symmetric spaces
$$\SLR n/\SO(n),\ \Sp(n,\R)/\UU(n),\ \SO^*(2n)/\UU(n),\ \SU^*(2n)/\Sp(n).$$
In each case, we produce a multidimensional parametrized family of complete minimal submanifolds of codimension two. The results form a continuation of the work in \cite{Geg-Gud-1}, which concerns the classical compact symmetric spaces.

The approach is largely elementary, accessible to readers with a basic background in differential geometry and Lie groups. Chapters \ref{ch:eigen} and \ref{ch:symmetric} serve as an introduction to the theory of eigenfunctions and Riemannian symmetric spaces, respectively. In Chapter \ref{ch:matrix} we establish some useful notation and definitions for working with matrix Lie groups. Finally, each of the Chapters \ref{ch:slr}, \ref{ch:spr}, \ref{ch:sox} and \ref{ch:sux} are dedicated to one of the symmetric spaces in question.}},
  author       = {{Larsen, Lucas}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences}},
  title        = {{Complete Minimal Submanifolds of Classical Non-Compact Riemannian Symmetric Spaces}},
  year         = {{2025}},
}