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Pontifical Catholic University of Rio de Janeiro

1. EDISON FAUSTO CUBA HUAMANI. [en] AFFINE MINIMAL SURFACES WITH SINGULARITIES.

Degree: 2017, Pontifical Catholic University of Rio de Janeiro

[pt] Neste trabalho, estudamos superfícies com curvatura média afim zero. Elas são chamadas de superfícies mínimas afins e para superfícies convexas, também são chamadas de superfícies máximas afins. Provamos que uma superfície mínima euclidiana também é uma superfície mínima afim se, e somente se, as linhas de curvatura da superfície mínima euclidiana conjugada são planas. Para uma superfície máxima afim, descrevemos como recuperá-la do campo de vetor conormal ao longo de uma determinada curva. Para algumas escolhas do vector conormal, a superfície máxima é singular e descrevemos as condições sob as quais as singularidades são arestas cuspidais ou swallowtails.

[en] In this work we study surfaces with zero affine mean curvature. They are called affine minimal surfaces and for convex surfaces, they are also called affine maximal surfaces. We prove that an euclidean minimal surface is also an affine minimal surface if and only if the curvature lines of the conjugate euclidean minimal surface are planar. For an affine maximal surface, we describe how to recover it from the conormal vector field along a given curve. For some choices of the conormal vector, the maximal surface is singular and we describe conditions under which the singularities are cuspidal edges or swallowtails.

Advisors/Committee Members: MARCOS CRAIZER.

Subjects/Keywords: [pt] LINHA DE CURVATURA PLANA; [en] PLANAR CURVATURE LINE; [pt] SUPERFICIES AFINS MINIMAS; [en] AFFINE MINIMAL SURFACES; [pt] SUPERFICIES AFINS MAXIMAS; [en] AFFINE MAXIMAL SURFACES; [pt] APLICACOES AFINS IMPROPIAS; [en] IMPROPER AFFINE MAPS; [pt] SWALLOWTAILS; [en] SWALLOWTAILS; [pt] CUSPIDAL EDGES; [en] CUSPIDAL EDGES

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

HUAMANI, E. F. C. (2017). [en] AFFINE MINIMAL SURFACES WITH SINGULARITIES. (Thesis). Pontifical Catholic University of Rio de Janeiro. Retrieved from http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32452

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

HUAMANI, EDISON FAUSTO CUBA. “[en] AFFINE MINIMAL SURFACES WITH SINGULARITIES.” 2017. Thesis, Pontifical Catholic University of Rio de Janeiro. Accessed September 25, 2018. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32452.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

HUAMANI, EDISON FAUSTO CUBA. “[en] AFFINE MINIMAL SURFACES WITH SINGULARITIES.” 2017. Web. 25 Sep 2018.

Vancouver:

HUAMANI EFC. [en] AFFINE MINIMAL SURFACES WITH SINGULARITIES. [Internet] [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2017. [cited 2018 Sep 25]. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32452.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

HUAMANI EFC. [en] AFFINE MINIMAL SURFACES WITH SINGULARITIES. [Thesis]. Pontifical Catholic University of Rio de Janeiro; 2017. Available from: http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32452

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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