Complete classification of surfaces with a canonical principal direction in the Euclidean space $$ \mathbb{E} $$ 3

• Autorzy: Marian Munteanu , Ana Nistor
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Canonical coordinates; Minimal surface; Euclidean 3-space

Kategorie tematyczne

• 53B25: Local submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 378-389

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Marian Munteanu

autor

Ana Nistor

Bibliografia

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• [5] Dillen F., Munteanu M.I., Nistor A.I., Canonical coordinates and principal directions for surfaces in \( \mathbb{H} \) 2×ℝ, Taiwanese J. Math., 2011 (in press), preprint available at http://arxiv.org/abs/0910.2135
• [6] Morita S., Geometry of Differential Forms, Transl. Math. Monogr., 201, American Mathematical Society, Providence, 2001
• [7] Munteanu M.I., Nistor A.-I., A new approach on constant angle surfaces in \( \mathbb{H} \) 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 \( \mathbb{S} \) n×ℝ and ℍn×ℝ, Illinois J. Math., 2011 (in press), preprint available at http://arxiv.org.abs/0909.2265

Identyfikatory

DOI

10.2478/s11533-011-0001-7