Anos (2004-2021)

Por Ronaldo Alves Atualizada em 17/02/26 07:37

2021.

Discovering Poncelet invariants in the plane. Paper from the 33rd Brazilian mathematics colloquium – 33°Colóquio Brasileiro de Matemática, IMPA, Rio de Janeiro, Brazil, August 2–6, 2021. Zbl 1511.14001

Publicações Matemáticas do IMPA. Rio de Janeiro: Instituto Nacional de Matemática Pura e Aplicada (IMPA) (ISBN 978-65-89124-43-6). 250 p., open access (2021).

Reznik, Dan; Garcia, Ronaldo

Related by similarity. II: Poncelet 3-periodics in the homothetic pair and the Brocard porism. bl 1513.51035

Int. J. Geom. 10, No. 4, 18-31 (2021).

MSC: 51M04 51N20

Garcia, Ronaldo; Reznik, Dan

Related by similarity. I: Poristic triangles and 3-periodics in the elliptic billiard. Zbl 1513.51019

Int. J. Geom. 10, No. 3, 52-70 (2021).

MSC: 51M04 51N20 51N35 68T20

Reznik, Dan; Garcia, Ronaldo

Intriguing invariants of centers of ellipse-inscribed triangles. (English) Zbl 1477.51008

J. Geom. 112, No. 2, Paper No. 28, 22 p. (2021).

Reviewer: Cătălin Barbu (Bačau)

MSC: 51M04 51N20 53A04

Garcia, Ronaldo; Reznik, Dan; Stachel, Hellmuth; Helman, Mark

Steiner’s hat: a constant-area deltoid associated with the ellipse. Zbl 1467.51011

KoG 24, 12-28 (2020).

da Cruz, Douglas H.; Garcia, Ronaldo A.

Finite type $ξ$ -asymptotic lines of plane fields in $R^{3}$ . Zbl 1458.53012

J. Singul. 22, 17-27 (2020).

Reznik, Dan S.; Garcia, Ronaldo; Koiller, Jair

The ballet of triangle centers on the elliptic billiard. Zbl 1453.37024

J. Geom. Graph. 24, No. 1, 79-101 (2020).

Reviewer: Thomas B. Ward (Leeds)

Reznik, Dan; Garcia, Ronaldo; Koiller, Jair

Can the elliptic billiard still surprise us? Zbl 1439.37031

Math. Intell. 42, No. 1, 6-17 (2020).

MSC: 37C83 37J40

Barajas, M.; Craizer, M.; Garcia, R.

Lines of affine principal curvatures of surfaces in 3-space. Zbl 1439.53012

Result. Math. 75, No. 1, Paper No. 32, 29 p. (2020).

Reviewer: Atsushi Fujioka (Osaka)

Craizer, Marcos; Garcia, Ronaldo A.

Quadratic points of surfaces in projective 3-space. Zbl 1455.53036

Q. J. Math. 70, No. 3, 1105-1134 (2019).

Garcia, Ronaldo Elliptic billiards and ellipses associated to the 3-periodic orbits. Zbl 1444.37023 Am. Math. Mon. 126, No. 6, 491-504 (2019).

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.

Listar Todas Voltar