Literatura académica sobre el tema "Immersion isométrique"
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Artículos de revistas sobre el tema "Immersion isométrique":
Labourie, François. "Immersions isométriques elliptiques et courbes pseudo-holomorphes". Journal of Differential Geometry 30, n.º 2 (1989): 395–424. http://dx.doi.org/10.4310/jdg/1214443596.
Schlenker, Jean-Marc. "Des immersions isométriques de surfaces aux variétés hyperboliques à bord convexe". Séminaire de théorie spectrale et géométrie 21 (2003): 165–216. http://dx.doi.org/10.5802/tsg.340.
Tesis sobre el tema "Immersion isométrique":
Zang, Yiming. "Les surfaces de Ricci et les surfaces minimales dans les groupes de Lie métriques". Thesis, Université de Lorraine, 2022. https://docnum.univ-lorraine.fr/ulprive/DDOC_T_2022_0115_ZANG.pdf.
In this thesis, we will study some topics related to minimal surfaces in three-dimensional homogeneous manifolds. The first part is devoted to the study of non-positively curved Ricci surfaces with catenodial ends. The idea comes from a famous theorem of Huber. In the first place, we give a definition of catenoidal end for non-positively curved Ricci surfaces with finite total curvature. Secondly, we develop a tool which can be regarded as an analogue of the Weierstrass data. By using this tool, we get some classification results and some non-existence results for non-positively curved Ricci surfaces of genus zero with catenoidal ends. In the end of Chapter 2, we also prove an existence result for non-positively curved Ricci surfaces of arbitrary positive genus with finite many catenoidal ends.In the second part of this thesis, we concern about minimal surfaces in a three-dimensional metric Lie group widetilde{E(2)}, which is the universal covering of the group of rigid motions of Euclidean plane endowed with a left-invariant Riemannian metric. Firstly, a result of Patrangenaru describes the left-invariant metrics as a two-parameter family of metrics. Then we take advantage of a Weierstrass-type representation due to Meeks, Mira, Pérez and Ros to construct a one-parameter family of helicoidal minimal surfaces in widetilde{E(2)} as well as a one-parameter family of minimal annuli which are properly embedded in widetilde{E(2)}. In the end, by a discussion of the limit case of the second family of surfaces, we obtain a new proof of a half-space theorem for minimal surfaces in widetilde{E(2)}
Mardare, Sorin. "Sur quelques problèmes de géométrie différentielle liés à la théorie de l'élasticité". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2003. http://tel.archives-ouvertes.fr/tel-00270549.
Dans les deux premiers chapitres, on montre que l'inégalité de Korn sur une surface est une conséquence de l'inégalité de Korn tridimensionnelle en coordonnées curvilignes et l'on établit une inégalité de type Korn sur une surface compacte sans bord. Dans le deux derniers chapitres, on établit certains résultats de géométrie différentielle concernant les espaces riemanniens et les surfaces sous des hypothèses affablies de régularité sur les données.
Dans l'appendice, on présente quelques résultats d'analyse utilisés dans la thèse.
Oliveira, Iury Rafael Domingos de. "Surfaces à courbure moyenne constante dans les variétés homogènes". Thesis, Université de Lorraine, 2020. http://www.theses.fr/2020LORR0057.
The goal of this thesis is to study constant mean curvature surfaces into homogeneous 3-manifolds with 4-dimensional isometry group. In the first part of this thesis, we study constant mean curvature surfaces in the product manifolds \mathbb{S}^2\times\mathbb{R} and \mathbb{H}^2\times\mathbb{R}. As a main result, we establish a local classification for constant mean curvature surfaces with constant intrinsic curvature in these spaces. In this classification, we present a new example of constant mean curvature surfaces with constant intrinsic curvature in \mathbb{H}^2\times\mathbb{R}. As a consequence, we use the sister surface correspondence to classify the constant mean curvature surfaces with constant intrinsic curvature in the others homogeneous 3-manifolds with 4-dimensional isometry group, and then new examples with these conditions arise in \widetilde{\mathrm{PSL}}_{2}(\mathbb{R}). We devote the second part of this thesis to study minimal surfaces in \mathbb{S}^2\times\mathbb{R}. For this, we define a new Gauss map for surfaces in this space using the model of \mathbb{S}^2\times\mathbb{R} isometric to \mathbb{R}^3\setminus\{0\}, endowed with a metric conformally equivalent to the Euclidean metric of \mathbb{R}^3. As a main result, we prove that any two minimal conformal immersions in \mathbb{S}^2\times\mathbb{R} with the same non-constant Gauss map differ by only two types of ambient isometries. Moreover, if the Gauss map is a singular, we show that it is necessarily constant and then the surface is a vertical cylinder over a geodesic of \mathbb{S}^2 in \mathbb{S}^2\times\mathbb{R}. We also study some particular cases, among them we also prove that there is no minimal conformal immersion into \mathbb{S}^2\times\mathbb{R} with anti-holomorphic non-constant Gauss map