Associate and conjugate minimal immersions in $\boldsymbol{M} \times \boldsymbol{R}$ - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Tohoku mathematical journal Année : 2008

Associate and conjugate minimal immersions in $\boldsymbol{M} \times \boldsymbol{R}$

Résumé

We establish the definition of associate and conjugate conformal minimal isometric immersions into the product spaces, where the first factor is it Riemannian surface and the other is the set of real numbers. When the Gaussian Curvature of the first factor is nonpositive. we prove that an associate surface of it minimal vertical graph over a convex domain is still a vertical graph. This generalizes a well-known result due to R. Krust. Focusing the case when the first factor is the hyperbolic plane, it is known that in certain class of surfaces, two minimal isometric immersions are associate. We show that this is not true in general. In the product ambient space, when the first factor is either the hyperbolic plane or the two-sphere, we prove that the conformal metric and the Hopf quadratic differential determine it simply connected minimal conformal immersion, up to an isometry of the ambient space. For these two product spaces, we derive the existence of the minimal associate family.
Fichier principal
Vignette du fichier
HET.pdf (625.01 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00693068 , version 1 (01-05-2012)

Licence

Domaine public

Identifiants

Citer

Laurent Hauswirth, Ricardo Sa Earp, Eric Toubiana. Associate and conjugate minimal immersions in $\boldsymbol{M} \times \boldsymbol{R}$. Tohoku mathematical journal, 2008, 60 (2), pp.267-286. ⟨10.2748/tmj/1215442875⟩. ⟨hal-00693068⟩
114 Consultations
94 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More