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 |
|---|---|
| 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| _version_ | 1862741052763406336 |
|---|---|
| author | Gorkavyy, V. |
| author_facet | Gorkavyy, V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | 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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| first_indexed | 2025-12-07T20:17:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106588 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-12-07T20:17:44Z |
| publishDate | 2006 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Gorkavyy, V. 2016-09-30T20:36:18Z 2016-09-30T20:36:18Z 2006 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. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106588 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. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type Article published earlier |
| spellingShingle | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type Gorkavyy, V. |
| title | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type |
| title_full | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type |
| title_fullStr | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type |
| title_full_unstemmed | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type |
| title_short | On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type |
| title_sort | on pseudospherical surfaces in e⁴ with grassmann image of prescribed type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106588 |
| work_keys_str_mv | AT gorkavyyv onpseudosphericalsurfacesine4withgrassmannimageofprescribedtype |