Últimos anos (2004-atual)

Por Ronaldo Alves Atualizada em 15/01/19 20:51
  • Garcia, Ronaldo; Evilson;  Vieira. Asymptotic behavior of the shape of planar polygons by linear flows.
    Linear Algebra Appl. 557 (2018), 508–528.
  • GARCIA, RONALDO; Freitas, Bruno. Inflections Points on Hyperbolic Tori of S3. 2018. Q. J. Math. 69 (2018), no. 2, 709–728. doi:10.1093/qmath/hax058 

  • GARCIA, RONALDO;  Sotomayor, J. . Historical Comments on Monge's Ellipsoid and the Configurations of Lines of Curvature on Surfaces, Elipsoid Mongea i konfiguracje linii krzywiznowych na powierzchniach i przestrzeniach euklidesowych - uwagi historyczne. Antiquitates Mathematicae, v. 10, p. 169-184, 2017.

  •  GARCIA, RONALDO;  LANGEVIN, RÉMI ; WALCZAK, PAWEL . Darboux curves on surfaces I. Journal of the Mathematical Society of Japan, v. 69, p. 1-24, 2017. 

  •  GARCIA, RONALDO; Sotomayor, J. . Lines of curvature on quadric hypersurfaces of R4. Lobachevskii Journal of Mathematics, v. 37, p. 288-306, 2016.

  • GARCIA, RONALDO; LANGEVIN, R. ; WALCZAK, PAWEL . Darboux curves on surfaces II. Sociedade Brasileira de Matematica. Boletim, Nova Serie, v. 47, p. 1119-1154, 2016.

  • Garcia, Ronaldo; Langevin, Remi, Walczak Pawel,   Foliations making a constant angle with principal directions on ellipsoids. Annales Polonici Mathematici, v. 113, p. 165-173, 2015.    
  • Garcia, Ronaldo, Lopes, Débora, Sotomayor Jorge.  Partially umbilic singularities of hyper surfaces of R4. Bulletin des Sciences Mathématiques v.139, (2015), pp. 431-472.
  • Garcia, Ronaldo, Spindola, Flausino,  Sotomayor Jorge; Axiumbilic Singular Points on Surfaces Immersed in R^4 and their Generic Bifurcations. Journal of Singularities, v. 10, p. 124-146, 2014.
  • Garcia, Ronaldo, Lopes, Débora, Sotomayor Jorge. Umbilic singularities and lines of curvature on ellipsoids of R4. Boletim da Sociedade Brasileira de Matematica. Nova Serie,  v. 45, p. 453-483, 2014. 
  • Garcia, Ronaldo; Marques, Diego; A family of minimal immersed tori in with dense principal lines. Bulletin des Sciences Mathématiques v.137, (2013), pp. 220- 227.
  • Garcia, Ronaldo, Dinâmica e Geometria, 2o.  Colóquio de Matemática da Região Nordeste, (2012), ISBN 978-85-7463-560-6, UFPI, 134 páginas.
  • Garcia, Ronaldo; Ferreira, Jocirei D.; Sree Hari Rao, V. Bifurcation dynamics: theory, methods, and applications [Editorial]. Differ. Equ. Dyn. Syst. 20 (2012), no. 3, 189–190. Editor de um volume especial.

  • GARCIA, Ronaldo Alves; Aspectos da História da Sociedade Brasileira de Matemática. Revista Brasileira de História da Matemática vol .11 (2012), 99 -109.

  • Garcia, Ronaldo; Sotomayor, Jorge; Lines of axial curvature at critical points on surfaces mapped into R4.  São Paulo J. Math. Sci. 6 (2012), no. 2, 277-300. 

  • Garcia, Ronaldo; Mello, Luis Fernado, Sotomayor, Jorge; Surfaces around closed principal curvature lines, an inverse problem. Real and Complex Singularities. London Math. Society, 2010, vol .380, p. 158- 166.

  • GARCIA, Ronaldo Alves,  SOTOMAYOR, J.,Tori embedded in R3 with dense principal lines. Bulletin des Sciences Mathématiques. , v.133, p.348 - 354, 2009. (arxiv)
  •  GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge Tori embedded in S3 with dense asymptotic lines. Anais da Academia Brasileira de Ciências. , v.81, p.13 - 19, 2009. (arxiv)
  •  GARCIA, Ronaldo Alves, LANGEVIN, R., George, Holonomy of a foliation by principal curvature lines. Boletim da Sociedade Brasileira de Matemática. , v.39, p.341 - 354, 2008.
  •  GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, Lines of Curvature on Surfaces, Historical Comments and Recent Developments. Sao Paulo Journal of Mathematical Sciences. , v.2, p.99 - 143, 2008. (arxiv)

  •  GARCIA, Ronaldo Alves. A trefoil has two or more vertices. Results in Mathematics / Resultate der Mathematik. , v.50, p.43 - 51, 2007.

  • GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, Codimension two umbilic points on surfaces immersed in R3 . Discrete and Continuous Dynamical Systems. Series A. , v.17, p.293 - 308, 2007. (arxiv)

  •  GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, Lines of Principal Curvature near Singular End Points of Surfaces in R3. Advanced Studies in Pure Mathematics (Amsterdam). , v.43, p.437 - 462, 2006. (arxiv)

  • GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, LLIBRE, Jaume, Lines of principal curvature on canal surfaces in R3 . Anais da Academia Brasileira de Ciências. , v.78, p.405 - 415, 2006. (arxiv)

  •   GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, On the Patterns of Principal Curvature Lines around a Curve of Umbilic Points. Anais da Academia Brasileira de Ciências. , v.77, p.13 - 24, 2005. (arxiv)

  •  GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, GUTIERREZ, Carlos, Bifurcations of Umbilic Points and Related Principal Cycles. Journal of Dynamics and Differential Equations. , v.16, p.321 - 346, 2004. (arxiv)
  •  GARCIA, Ronaldo Alves, SOTOMAYOR, Jorge, Lines of Mean Curvature on Surfaces Immersed in R3. Qualitative Theory of Dynamical Systems. , v.05, p.263 - 309, 2004. (arxiv)

  •  GARCIA, Ronaldo Alves, On the 60th birthday of Jorge Sotomayor. Qualitative Theory of Dynamical Systems. , v.05, p.01 - 03, 2004.
  •   GARCIA, Ronaldo Alves, TEIXEIRA, Marco Antonio, Vector fields on manifolds with boundary and reversibility - An expository account. Qualitative Theory of Dynamical Systems , v.05, p.185 - 200, 2004.
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