Unduloids and their geometry

Mariana Hadzhilazova; Ivaïlo M. Mladenov; John Oprea

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 5, page 417-429
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Hadzhilazova, Mariana, Mladenov, Ivaïlo M., and Oprea, John. "Unduloids and their geometry." Archivum Mathematicum 043.5 (2007): 417-429. <http://eudml.org/doc/250167>.

@article{Hadzhilazova2007,
abstract = {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.},
author = {Hadzhilazova, Mariana, Mladenov, Ivaïlo M., Oprea, John},
journal = {Archivum Mathematicum},
keywords = {mean curvature; unduloid; mean curvature; unduloid},
language = {eng},
number = {5},
pages = {417-429},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Unduloids and their geometry},
url = {http://eudml.org/doc/250167},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Hadzhilazova, Mariana
AU - Mladenov, Ivaïlo M.
AU - Oprea, John
TI - Unduloids and their geometry
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 5
SP - 417
EP - 429
AB - 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.
LA - eng
KW - mean curvature; unduloid; mean curvature; unduloid
UR - http://eudml.org/doc/250167
ER -

References

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  7. Isenberg C., The Science of Soap Films and Soap Bubbles, Dover, New York, 1992. (1992) 
  8. Janhke E., Emde F., Lösch F., Tafeln höherer Funktionen, Teubner, Stuttgart, 1960. (1960) 
  9. Kenmotsu K., Surfaces of revolution with prescribed mean curvature, Thoku Math. J. 32 (1980), 147–153. (1980) Zbl0431.53005MR0567837
  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. Zbl1051.53005MR1977569
  11. Mladenov I., Oprea J., The Mylar balloon: New viewpoints and generalizations, In: Geometry, Integrability and Quantization VIII, SOFTEX, Sofia, 2007, 246–263. Zbl1123.53006MR2341209
  12. Oprea J., Differential Geometry and Its Applications, Mathematical Association of America, Washington D. C., 2007. Zbl1153.53001MR2327126

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