On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type
It is demonstrated that there exist surfaces of constant negative Gauss curvature in E⁴ whose Grassmann image consists of either hyperbolic or parabolic or elliptic points. As a consequence, there exist surfaces of constant negative Gauss curvature in E⁴ which do not admit Backlund transformations w...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2006 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106588 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type / V. Gorkavyy // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 2. — С. 138-148. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | It is demonstrated that there exist surfaces of constant negative Gauss curvature in E⁴ whose Grassmann image consists of either hyperbolic or parabolic or elliptic points. As a consequence, there exist surfaces of constant negative Gauss curvature in E⁴ which do not admit Backlund transformations with help of pseudospherical congruencies. A geometric representation for pseudospherical surfaces in E⁴ with parabolic Grassmann image is proposed.
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| ISSN: | 1812-9471 |