Rui Pacheco
Departamento de Matemática da Universidade da Beira Interior.
Covilhã, Portugal
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Publications:
Differential Geometry
R. Pacheco and S. D. Santos, On congruences of Laguerre cycles and their envelopes. Submitted, 2020.
A. Aleman, R. Pacheco, and J. C. Wood, Symmetric shift-invariant subspaces and harmonic maps . Submitted, 2019.
N. Correia, R. Pacheco and M. Svensson, Harmonic surfaces in the Cayley Plane. To appear in the Journal of the London Mathematical Society.
R. Pacheco and S. D. Santos, Envelopes of circles and spacelike curves in the Lorentz-Minkowski 3-space. Forum Math. 32 (2020), no. 3, 693–711.
A. Aleman, R. Pacheco, and J. C. Wood, Harmonic maps and shift-invariant subspaces . Submitted, 2019.
R. Pacheco, Isothermic surfaces from harmonic maps in S^6 . Publications De L'Institut Mathemátique, Nouvelle série, tome 103(117) (2018), 175–180.
P. Morais and R. Pacheco, Surfaces in R^7 obtained from harmonic maps in S^6. Geom. Dedicata 194 (2018), 65–80.
B. Nolasco and R. Pacheco, Evolutes of plane curves and null curves in Minkowski 3-space. J. Geom. 108 (2017), no. 1, 195–214.
N. Correia and R. Pacheco, Harmonic spheres in outer symmetric spaces, their canonical elements and Weierstrass type representations , Manuscripta Math. 152 (2017), no. 3-4, 399–432.
N. Correia and R. Pacheco, Harmonic maps of finite uniton number and their canonical elements, Annals of Global Analysis and Geometry, April 2015, Volume 47, Issue 4, 335-358.
N. Correia and R. Pacheco, Extended solution to the harmonic map equation into SU(n), Q. J. Math. 65, no. 2, 637–654, 2014.
R. Pacheco, Immersed surfaces in Lie algebras associated to primitive harmonic maps. Geometriae Dedicata 163, 379-390, 2013.
R. Pacheco, Index and nullity of a family of harmonic tori in the sphere, Advances in Geometry, Volume 13, Issue 13, 381-388, 2013.
N. Correia and R. Pacheco, Harmonic maps of finite uniton number into G_2, Math. Z. 271, nº 1-2, 13-32, 2012.
N. Correia and R. Pacheco, Singular dressing actions on harmonic maps. Q. J. Math. 62 (1), 71-85, 2011.
R. Pacheco, Bianchi-Backlund transforms and dressing actions, Geometriae Dedicata, Volume 146, Number 1, June, 85-99, 2010.
N. Correira and R. Pacheco, Adding a uniton via DPW method, International Journal of Mathematics. 20, no. 8, 997-1010, 2009.
R. Pacheco, On harmonic tori in compact rank one symmetric spaces, Differential Geometry and its Applications. Vol. 27, Issue 3, 352-361, 2009.
R. Pacheco, Harmonic two-spheres in the symplectic group Sp(n), International Journal of Mathematics. Vol. 17, No.3, 295-311, 2006.
R. Pacheco, Twistor fibrations giving primitive harmonic maps of finite type , International Journal of Mathematics and Mathematical Sciences. Volume 2005, Number 20, 3199-3212, 2005.
Other Publications
S. M. M. Rasouli, R. Pacheco, M. Sakellariadou, P. V. Moniz, Late time cosmic acceleration in modified Sáez-Ballester theory. Phys.Dark Univ. 27 (2020)
A. Bernardino, R. Pacheco and M. Silva, Coloring Factors of Substitutive Infinite Words. Discrete Math. 340 (2017), no. 3, 443–451.
A. Bernardino, R. Pacheco and M. Silva, The gap structure of a family of integer subsets, Electronic Journal of Combinatorics, Vol 21, Issue 1 (2014) P1.47.
R. Pacheco e M. Raposo, Geometria do Sistema Temperado, Gazeta de Matemática. Nº174, Novembro 2014.
R. Pacheco and H. Vilarinho, Statistical Stability for Multi-Substitution Tiling Spaces, Discrete Contin. Dyn. Syst. 33, nº 10, 4589-4594, 2013.
R. Pacheco and H. Vilarinho, Metrics on tiling spaces, local isomorphism and an application of Brown's lemma, Monatshefte für Mathematik 170. nº 2, 205-225, 2013.
R. Pacheco. F. Pinheiro and R. Portugal, A note on the geometry of three circles, Creat. Math. Inform. 20 (1), 74-80, 2011.
R. Pacheco, Rosetas, Gazeta de Matemática. Nº156, Novembro 2008.
Thesis:
Harmonic Maps and Loop Groups. PhD. University of Bath, 2004. (Orientador: Fran Burstall).
Aplicações harmónicas de superfícies de Riemann em variedades Riemannianas de Dimensão 4. Mestrado em Matemática. Faculdade de Ciências da Universidade de Lisboa, 1999. (Orientador: Armando Machado).
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