From the 1 of 6 linked papers with an AI index.
6 papers
New Complex-Valued Harmonic Morphisms via Rational Exponents
Sigmundur Gudmundsson
The method of complex-valued eigenfamilies has been used to solve difficult non-linear problems in differential geometry. The purpose of this note is to generalise the construction…
New Minimal Surfaces of the Sphere and the Hyperbolic Space via Harmonic Morphisms
Sigmundur Gudmundsson, Leonard Nygren Löhndorf
The paper presents a new method using complex-valued harmonic morphisms to construct explicit minimal codimension‑two submanifolds in the 4‑sphere and 4‑dimensional hyperbolic spac…
Minimal Submanifolds of The Complex and Quaternionic Projective and Hyperbolic Spaces $\cn P^{2n-1}$, $\hn P^{2n-1}$, $\cn H^{2n-1}$, $\hn H^{2n-1}$ via Harmonic Morphisms
Sigmundur Gudmundsson
In this work we construct non-holomorphic, complete and minimal submanifolds of the odd-dimensional complex projective spaces $\cn P^{2n-1}$ and their dual complex hyperbolic space…
Complete minimal submanifolds of the non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(2n)/U(n), SU*(2n)/Sp(n) via complex-valued eigenfunctions
Sigmundur Gudmundsson, Lucas Larsen
In this work we construct new multidimensional families of complete minimal submanifolds, of the classical non-compact Riemannian symmetric spaces SL_n(R)/SO(n), Sp(n,R)/U(n), SO*(…
Harmonic Morphisms and Minimal Conformal Foliations on Lie Groups
Sigmundur Gudmundsson, Thomas Jack Munn
Let be a Lie group equipped with a left-invariant Riemannian metric. Let be a semisimple and normal subgroup of generating a left-invariant conformal foliation $\F$ of…
A Unifying Framework for Complex-Valued Eigenfunctions via The Cartan Embedding
Sigmundur Gudmundsson, Adam Lindström
In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known…