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HARMONIC TWO-SPHERES IN THE SYMPLECTIC GROUP Sp(n)

- R. Pacheco
- Mathematics
- 1 March 2006

We shall exploit the Grassmannian theoretic point of view introduced by Segal in order to study harmonic maps from a two-sphere into the symplectic group Sp(n). By using this methodology, we shall be… Expand

Harmonic maps of finite uniton number into G2

- N. Correia, R. Pacheco
- Mathematics
- 26 July 2010

We establish explicit formulae for canonical factorizations of extended solutions corresponding to harmonic maps of finite uniton number into the exceptional Lie group G2 in terms of the Grassmannian… Expand

On harmonic tori in compact rank one symmetric spaces

- R. Pacheco
- Mathematics
- 1 June 2009

Abstract In this paper we prove that, in contrast with the S n and C P n cases, there are harmonic 2-tori into the quaternionic projective space H P n which are neither of finite type nor of finite… Expand

Evolutes of plane curves and null curves in Minkowski 3-space

- Boaventura Nolasco, R. Pacheco
- Mathematics
- 6 May 2016

We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski 3-space. We describe the geometry of null curves… Expand

Harmonic maps of finite uniton number and their canonical elements

- N. Correia, R. Pacheco
- Mathematics
- 15 May 2014

We classify all harmonic maps with finite uniton number from a Riemann surface into an arbitrary compact simple Lie group $$G$$G, whether $$G$$G has trivial centre or not, in terms of certain pieces… Expand

Harmonic maps and shift-invariant subspaces

- A. Aleman, R. Pacheco, J. Wood
- Mathematics
- 21 December 2018

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models which are families of shift-invariant subspaces of… Expand

Index and nullity of a family of harmonic tori in the sphere

- R. Pacheco
- Mathematics
- 22 February 2012

In this note we investigate the $(E)$-index and the $(E)$-nullity of vacuum solutions from the two-torus into the two sphere.

Statistical Stability for Multi-Substitution Tiling Spaces

- R. Pacheco, H. Vilarinho
- Mathematics
- 16 July 2012

Given a finite set ${S_1...,S_k}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\rd$, we consider the multi-substitution tiling space associated to each… Expand

Bianchi–Bäcklund transforms and dressing actions, revisited

- R. Pacheco
- Mathematics
- 29 August 2008

We characterize Bianchi–Bäcklund transformations of surfaces of positive constant Gauss curvature in terms of dressing actions of the simplest type on the space of harmonic maps.

Adding a uniton via the DPW method

- N. Correia, R. Pacheco
- Mathematics
- 10 December 2007

In this paper we describe how the operation of adding a uniton arises via the DPW method of obtaining harmonic maps into compact Riemannian symmetric spaces out of certain holomorphic one forms. We… Expand

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