Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 006, 13 pages      arXiv:0802.2438      https://doi.org/10.3842/SIGMA.2010.006

Peterson's Deformations of Higher Dimensional Quadrics

Ion I. Dincă
Faculty of Mathematics and Informatics, University of Bucharest, 14 Academiei Str., 010014, Bucharest, Romania

Received July 13, 2009, in final form January 16, 2010; Published online January 20, 2010

Abstract
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.

Key words: Peterson's deformation; higher dimensional quadric; common conjugate system.

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