Canonical Coordinates and Principal Directions for Surfaces in $\H^2\times\R$

Franki Dillen; Marian Ioan Munteanu; Ana Irina Nistor

Canonical Coordinates and Principal Directions for Surfaces in $\H^2\times\R$

Differential Geometry 2012-01-24 v2

Authors: Franki Dillen , Marian Ioan Munteanu , Ana Irina Nistor

Abstract

In this paper we characterize and classify surfaces in ${\mathbb{H}}^2\times{\mathbb{R}}$ which have a canonical principal direction. Here ${\mathbb{H}}^2$ denotes the hyperbolic plane. We study some geometric properties such as minimality and flatness. Some examples are given to complete the study.

Keywords

surfaces canonical principal direction hyperbolic plane minimal surfaces flat surfaces classification

Cite

@article{arxiv.0910.2135,
  title  = {Canonical Coordinates and Principal Directions for Surfaces in $\H^2\times\R$},
  author = {Franki Dillen and Marian Ioan Munteanu and Ana Irina Nistor},
  journal= {arXiv preprint arXiv:0910.2135},
  year   = {2012}
}

Comments

25 Latex pages, to appear in Taiwanese Mathematical Journal

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