On the isotropic group of a homogeneous polynomial
HTML articles powered by AMS MathViewer
- by Siu Ming Ho PDF
- Trans. Amer. Math. Soc. 183 (1973), 495-498 Request permission
Abstract:
Let G be the linear group leaving a homogeneous polynomial of degree k fixed. The author shows that either the polynomial is a polynomial in fewer than the assigned number of variables or that the $(k - 1)$st prolongation of G is 0. The author also shows that this result is optimal.References
- P. Gordan and M. Nöther, Ueber die algebraischen Formen, deren Hesse’sche Determinante identisch verschwindet, Math. Ann. 10 (1876), no. 4, 547–568 (German). MR 1509898, DOI 10.1007/BF01442264
- Victor Guillemin and Isadore M. Singer, Differential equations and $G$-structures, Proc. U.S.-Japan Seminar in Differential Geometry (Kyoto, 1965) Nippon Hyoronsha, Tokyo, 1966, pp. 34–36. MR 0213988
- I. M. Singer and Shlomo Sternberg, The infinite groups of Lie and Cartan. I. The transitive groups, J. Analyse Math. 15 (1965), 1–114. MR 217822, DOI 10.1007/BF02787690
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 183 (1973), 495-498
- MSC: Primary 53C10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0338987-6
- MathSciNet review: 0338987