Vertical Helicoids and Catenoids in $M\times\mathbb{R}$
de Lima, Ronaldo Freire ; Roitman, Pedro
arXiv, Tome 2019 (2019) no. 0, / Harvested from
Given an arbitrary $C^\infty$ Riemannian manifold $M^n$, we consider the problem of constructing minimal hypersurfaces in $M\times\mathbb{R}$ which have the same fundamental properties of the standard helicoids and catenoids of Euclidean space $\mathbb{R}^3$. We call them vertical helicoids and vertical catenoids. We establish necessary and sufficient conditions on $M$ for the existence of such minimal hypersurfaces, and also develop general methods for their construction.
Publié le : 2019-01-23
Classification:  Mathematics - Differential Geometry 
@article{1901.07936,
     author = {de Lima, Ronaldo Freire and Roitman, Pedro},
     title = {Vertical Helicoids and Catenoids in $M\times\mathbb{R}$},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.07936}
}

de Lima, Ronaldo Freire; Roitman, Pedro. Vertical Helicoids and Catenoids in $M\times\mathbb{R}$. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.07936/