On Ribaucour transformations and applications to linear Weingarten surfaces
Fuente:
Redalyc
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Artículo científico |
| Langue: | en |
| Publié: |
Academia Brasileira de Ciências
2002
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1876423191525588992 |
|---|---|
| author | Keti Tenenblat |
| author_facet | Keti Tenenblat |
| contents | On Ribaucour transformations and applications to linear Weingarten surfaces Keti Tenenblat Multidisciplinaria (Ciencias Naturales y Exactas) minimal surfaces constant mean curvature Ribaucour transformations linear Weingarten surfaces We present a revised definition of a Ribaucour transformation for submanifolds of space forms,with flat normal bundle, motivated by the classical definition and by more recent extensions.The new definition provides a precise treatment of the geometric aspect of such transformationspreserving lines of curvature and it can be applied to submanifolds whose principal curvatureshave multiplicity bigger than one. Ribaucour transformations are applied as a method of obtaininglinear Weingarten surfaces contained in Euclidean space, from a given such surface. Examplesare included for minimal surfaces, constant mean curvature and linear Weingarten surfaces. Theexamples show the existence of complete hyperbolic linear Weingarten surfaces in Euclideanspace. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774401 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.4 Vol.74 |
| format | Artículo científico |
| id | redalyc_32774401 |
| institution | Redalyc |
| language | en |
| publishDate | 2002 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | On Ribaucour transformations and applications to linear Weingarten surfaces Keti Tenenblat Multidisciplinaria (Ciencias Naturales y Exactas) minimal surfaces constant mean curvature Ribaucour transformations linear Weingarten surfaces On Ribaucour transformations and applications to linear Weingarten surfaces Keti Tenenblat Multidisciplinaria (Ciencias Naturales y Exactas) minimal surfaces constant mean curvature Ribaucour transformations linear Weingarten surfaces We present a revised definition of a Ribaucour transformation for submanifolds of space forms,with flat normal bundle, motivated by the classical definition and by more recent extensions.The new definition provides a precise treatment of the geometric aspect of such transformationspreserving lines of curvature and it can be applied to submanifolds whose principal curvatureshave multiplicity bigger than one. Ribaucour transformations are applied as a method of obtaininglinear Weingarten surfaces contained in Euclidean space, from a given such surface. Examplesare included for minimal surfaces, constant mean curvature and linear Weingarten surfaces. Theexamples show the existence of complete hyperbolic linear Weingarten surfaces in Euclideanspace. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774401 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.4 Vol.74 |
| title | On Ribaucour transformations and applications to linear Weingarten surfaces |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) minimal surfaces constant mean curvature Ribaucour transformations linear Weingarten surfaces |
| url | https://www.redalyc.org/articulo.oa?id=32774401 |