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 タイトル: Umbilical Points of the Graphs of Homogeneous Polynomials of Degree 3 著者: Ando, Naoya 発行日: 2001年 出版者: Graduate School of Mathematical Sciences, The University of Tokyo 掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 8 (2001), No. 1, Page 71-87 抄録: Let $P^3_o$ be the set of the homogeneous polynomials of degree $3$ such that on their graphs, the origin $o:=(0, 0, 0)$ of {\bf R}$^3$ is isolated as an umbilical point, and $P^{3,1/2}_o , P^{3,-1/2}_o$ the sets of the elements of $P^3_o$ such that on their graphs, the index of $o$ is equal to $1/2, -1/2$, respectively. In this paper, it is seen that $P^3_o$ is divided into $P^{3,1/2}_o$ and $P^{3,-1/2}_o$ by the cone obtained from a rectangular torus in the vector space of the homogeneous polynomials of degree $3$. URI: http://hdl.handle.net/2261/1196 ISSN: 13405705 出現カテゴリ: Journal of Mathematical Sciences, the University of TokyoJournal of Mathematical Sciences, the University of Tokyo

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