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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Volumes e curvaturas médias na geometria de Finsler:superfícies mínimas / Volumes and means curvatures in Finsler geometry: minimal surfaces

Chavéz, Newton Mayer Solorzano 16 April 2012 (has links)
Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-08-06T11:17:00Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Volumes_e_curvaturas_medias_na_geometria_de_finsler.pdf: 818570 bytes, checksum: fce77ff7f92ae9cc2bf9af2aa0318c4c (MD5) / Made available in DSpace on 2014-08-06T11:17:00Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Volumes_e_curvaturas_medias_na_geometria_de_finsler.pdf: 818570 bytes, checksum: fce77ff7f92ae9cc2bf9af2aa0318c4c (MD5) Previous issue date: 2012-04-16 / In Finsler geometry, we have several volume forms, hence various of mean curvature forms. The two best known volumes forms are the Busemann-Hausdorff and Holmes- Thompson volume form. The minimal surface with respect to these volume forms are called BH-minimal and HT-minimal surface, respectively. Let (R3; eFb) be a Minkowski space of Randers type with eFb = ea+eb; where ea is the Euclidean metric and eb = bdx3; 0 < b < 1: If a connected surface M in (R3; eFb) is minimal with respect to both volume forms Busemann-Hausdorff and Holmes-Thompson, then up to a parallel translation of R3; M is either a piece of plane or a piece of helicoid which is generated by lines screwing along the x3-axis. Furthermore it gives an explicit rotation hypersurfaces BH-minimal and HT-minimal generated by a plane curve around the axis in the direction of eb] in Minkowski (a;b)-space (Vn+1; eFb); where Vn+1 is an (n+1)-dimensional real vector space, eFb = eaf eb ea ; ea is the Euclidean metric, eb is a one form of constant length b = kebkea; eb] is the dual vector of eb with respect to ea: As an application, it give us an explicit expression of surface of rotation “ forward” BH-minimal generated by the rotation around the axis in the direction of eb] in Minkowski space of Randers type (V3; ea+eb): / Na Geometria de Finsler, temos várias formas volume, consequentemente várias formas curvaturas médias. As duas mais conhecidas são as formas de volumes Busemann- Hausdorff e Holmes-Thompson. As superfícies mínimas com respeito a estes são chamados superfícies BH-mínimas e HT-mínimas, respectivamente. Seja (R3; eFb) um espaço de Minkowski do tipo Randers com eFb = ea+eb; onde ea é a métrica Euclidiana e eb = bdx3;0 < b < 1: Uma superfície em (R3; eFb) conexa M é mínima com respeito a ambas formas volumes Busemann-Hausdorff e Holmes-Thompson, então a menos de uma translação paralela de R3; M é parte de um plano ou parte de um helicóide, a qual é gerada pela rotação de uma reta (perpendicular ao eixo x3) ao longo do eixo x3: Ademais podemos obter explicitamente hipersuperfícies de rotação BH-mínima e HT-mínima geradas por uma curva plana em torno do eixo na direção de eb] num espaço (a; b) de Minkowski (Vn+1; eFb); onde Vn+1 é um espaço vetorial de dimensão (n+1); eFb = eaf eb ea ; ea é a métrica Euclidiana, eb é uma 1-forma constante com norma b := kebkea; eb] é o vetor dual de eb com respeito a a: Como aplicação, se dá uma expressão explícita de superfície de rotação completa “forward” BH-mínima gerada pela rotação em torno do eixo na direção de eb] num espaço de Minkowski do tipo Randers (V3; ea+eb):

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