Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation
Abstract The mapping between Belavin–Polyakov (BP) equation for the evolution of a unit tangent vector T∈S2 $T\in \mathbb{S}^{2}$ of a space curve in R3 $\mathbb{R}^{3}$ and the elliptic Liouville equation has been shown by Balakrishnan (see Phys. Lett. A 204:243–246, 1995). In the present work, thi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-08-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1765-x |
| _version_ | 1818480166464126976 |
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| author | Shiping Zhong |
| author_facet | Shiping Zhong |
| author_sort | Shiping Zhong |
| collection | DOAJ |
| description | Abstract The mapping between Belavin–Polyakov (BP) equation for the evolution of a unit tangent vector T∈S2 $T\in \mathbb{S}^{2}$ of a space curve in R3 $\mathbb{R}^{3}$ and the elliptic Liouville equation has been shown by Balakrishnan (see Phys. Lett. A 204:243–246, 1995). In the present work, this result is effectively extended by mapping the BP equation for the unit tangent T∈S6 $T\in \mathbb{S}^{6}$ of a space curve in R7 $\mathbb{R}^{7}$ to the vector elliptic Liouville equation. To show this correspondence, Spin(7) $\operatorname{Spin}(7)$-frame field on the curve is used. |
| first_indexed | 2024-12-10T11:19:49Z |
| format | Article |
| id | doaj.art-bba4a062fc28478cb669a07a0942aab6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T11:19:49Z |
| publishDate | 2018-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-bba4a062fc28478cb669a07a0942aab62022-12-22T01:51:02ZengSpringerOpenAdvances in Difference Equations1687-18472018-08-012018111310.1186/s13662-018-1765-xSpin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equationShiping Zhong0School of Mathematical Sciences, Fudan UniversityAbstract The mapping between Belavin–Polyakov (BP) equation for the evolution of a unit tangent vector T∈S2 $T\in \mathbb{S}^{2}$ of a space curve in R3 $\mathbb{R}^{3}$ and the elliptic Liouville equation has been shown by Balakrishnan (see Phys. Lett. A 204:243–246, 1995). In the present work, this result is effectively extended by mapping the BP equation for the unit tangent T∈S6 $T\in \mathbb{S}^{6}$ of a space curve in R7 $\mathbb{R}^{7}$ to the vector elliptic Liouville equation. To show this correspondence, Spin(7) $\operatorname{Spin}(7)$-frame field on the curve is used.http://link.springer.com/article/10.1186/s13662-018-1765-xSpin ( 7 ) $\operatorname{Spin}(7)$ -structure equationOctonionsAlmost complex structureThe vector elliptic Liouville equation |
| spellingShingle | Shiping Zhong Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation Advances in Difference Equations Spin ( 7 ) $\operatorname{Spin}(7)$ -structure equation Octonions Almost complex structure The vector elliptic Liouville equation |
| title | Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation |
| title_full | Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation |
| title_fullStr | Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation |
| title_full_unstemmed | Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation |
| title_short | Spin(7) $\operatorname{Spin}(7)$-structure equation and the vector elliptic Liouville equation |
| title_sort | spin 7 operatorname spin 7 structure equation and the vector elliptic liouville equation |
| topic | Spin ( 7 ) $\operatorname{Spin}(7)$ -structure equation Octonions Almost complex structure The vector elliptic Liouville equation |
| url | http://link.springer.com/article/10.1186/s13662-018-1765-x |
| work_keys_str_mv | AT shipingzhong spin7operatornamespin7structureequationandthevectorellipticliouvilleequation |