| Title:
|
Unduloids and their geometry (English) |
| Author:
|
Hadzhilazova, Mariana |
| Author:
|
Mladenov, Ivaïlo M. |
| Author:
|
Oprea, John |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
2007 |
| Pages:
|
417-429 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider non-compact cylinder-like surfaces called unduloids and study some aspects of their geometry. In particular, making use of a Kenmotsu-type representation of these surfaces, we derive explicit formulas for the lengths and areas of arbitrary segments, along with a formula for the volumes enclosed by them. (English) |
| Summary:
|
ï () |
| Keyword:
|
mean curvature |
| Keyword:
|
unduloid |
| MSC:
|
49Q10 |
| MSC:
|
53-04 |
| MSC:
|
53A05 |
| MSC:
|
53C42 |
| MSC:
|
53Cxx |
| idZBL:
|
Zbl 1199.53008 |
| idMR:
|
MR2381785 |
| . |
| Date available:
|
2008-06-06T22:52:02Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108081 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[9] Kenmotsu K.: Surfaces of revolution with prescribed mean curvature.T$\hat{\mml@font@upright o}$hoku Math. J. 32 (1980), 147–153. Zbl 0431.53005, MR 0567837 |
| Reference:
|
[10] Mladenov I., Oprea J.: Unduloids and their closed geodesics.In: Proceedings of the Fourth International Conference on Geometry, Integrability and Quantization, Coral Press, Sofia, 2003, 206–234. Zbl 1051.53005, MR 1977569 |
| Reference:
|
[11] Mladenov I., Oprea J.: The Mylar balloon: New viewpoints and generalizations.In: Geometry, Integrability and Quantization VIII, SOFTEX, Sofia, 2007, 246–263. Zbl 1123.53006, MR 2341209 |
| Reference:
|
[12] Oprea J.: Differential Geometry and Its Applications.Mathematical Association of America, Washington D. C., 2007. Zbl 1153.53001, MR 2327126 |
| . |
