Peterson's Deformations of higher dimensional quadrics
We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in C³ of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the comp...
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| Date: | 2010 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2010
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146115 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Peterson's Deformations of higher dimensional quadrics / Dincă I.I. // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We provide the first explicit examples of deformations of higher dimensional quadrics: a straightforward generalization of Peterson's explicit 1-dimensional family of deformations in C³ of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere S² ⊂ C³ to an explicit (n–1)-dimensional family of deformations in C²ⁿ⁻¹ of n-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere Sⁿ ⊂ Cⁿ⁺¹ and non-degenerate joined second fundamental forms. It is then proven that this family is maximal. |
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