Geodesic
Peterson's Deformations of Higher Dimensional Quadrics
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathbb C^3$ of 2-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\mathbb S^2\subset\mathbb C^3$ to an explicit $(n-1)$-dimensional family of deformations in $\mathbb C^{2n-1}$ of $n$-dimensional general quadrics with common conjugate system given by the spherical coordinates on the complex sphere $\mathbb S^n\subset\mathbb C^{n+1}$ and non-degenerate joined second fundamental forms. It is then proven that this family is maximal.
Keywords: Peterson's deformation; higher dimensional quadric; common conjugate system. 
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     author = {Ion I. Dinc\u{a}},
     title = {Peterson's {Deformations} of {Higher} {Dimensional} {Quadrics}},
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     language = {en},
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Ion I. Dincă. Peterson's Deformations of Higher Dimensional Quadrics. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a5/

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