Complete classification of surfaces with a canonical principal direction in the Euclidean space 3
Open Mathematics (2011)
- Volume: 9, Issue: 2, page 378-389
- ISSN: 2391-5455
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topMarian Munteanu, and Ana Nistor. "Complete classification of surfaces with a canonical principal direction in the Euclidean space \[ \mathbb {E} \] 3." Open Mathematics 9.2 (2011): 378-389. <http://eudml.org/doc/269808>.
@article{MarianMunteanu2011,
abstract = {In the present paper we classify all surfaces in \[ \mathbb \{E\} \]
3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space \[ \mathbb \{E\} \]
3 is the catenoid.},
author = {Marian Munteanu, Ana Nistor},
journal = {Open Mathematics},
keywords = {Canonical coordinates; Minimal surface; Euclidean 3-space; canonical coordinates; minimal surface},
language = {eng},
number = {2},
pages = {378-389},
title = {Complete classification of surfaces with a canonical principal direction in the Euclidean space \[ \mathbb \{E\} \] 3},
url = {http://eudml.org/doc/269808},
volume = {9},
year = {2011},
}
TY - JOUR
AU - Marian Munteanu
AU - Ana Nistor
TI - Complete classification of surfaces with a canonical principal direction in the Euclidean space \[ \mathbb {E} \] 3
JO - Open Mathematics
PY - 2011
VL - 9
IS - 2
SP - 378
EP - 389
AB - In the present paper we classify all surfaces in \[ \mathbb {E} \]
3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space \[ \mathbb {E} \]
3 is the catenoid.
LA - eng
KW - Canonical coordinates; Minimal surface; Euclidean 3-space; canonical coordinates; minimal surface
UR - http://eudml.org/doc/269808
ER -
References
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- [4] Dillen F., Fastenakels J., Van der Veken J., Surfaces in 2×ℝ with a canonical principal direction, Ann. Global Anal. Geom., 2009, 35(4), 381–396 http://dx.doi.org/10.1007/s10455-008-9140-x Zbl1176.53031
- [5] Dillen F., Munteanu M.I., Nistor A.I., Canonical coordinates and principal directions for surfaces in 2×ℝ, Taiwanese J. Math., 2011 (in press), preprint available at http://arxiv.org/abs/0910.2135 Zbl1241.53010
- [6] Morita S., Geometry of Differential Forms, Transl. Math. Monogr., 201, American Mathematical Society, Providence, 2001 Zbl0987.58002
- [7] Munteanu M.I., Nistor A.-I., A new approach on constant angle surfaces in 3, Turkish J. Math., 2009, 33(2), 169–178
- [8] O’Neill B., Elementary Differential Geometry, 2nd ed. revised, Academic Press, Amsterdam, 2006
- [9] Tojeiro R., On a class of hypersurfaces in n×ℝ and ℍn×ℝ, Illinois J. Math., 2011 (in press), preprint available at http://arxiv.org.abs/0909.2265
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