View from inside
スポンサーリンク
概要
- 論文の詳細を見る
In this paper, we define a perspective projection of a given immersed n-dimensional hypersurface as a C^∞ map via a C^∞ immersion from the given n-manifold to S^$n+1$, and characterize when and only when such a perspective projection is nonsingular. In order to obtain such characterizations, we consider an immersion from an n-dimensional manifold to S^$n+1$. We first obtain equivalent conditions for a given point P of S^$n+1$ to be outside the union of tangent great hyperspheres of a given immersed n-dimensional manifold r(N) in S^$n+1$ (Theorem 2.4). It turns out that if such a point P exists then the given manifold N must be diffeomorphic to S^n and in the case that n\geq2 the given immersion r:N→S^$n+1$ must be an embedding. Then, we obtain characterizations of a perspective projection of a given immersed n-dimensional manifold to be non-singular. Next, we obtain one more equivalent condition in terms of hedgehogs when the given N is S^n and the given immersion is an embedding (Theorem 3.3). We also explain why we consider these equivalent conditions for an embedding r:S^n→S^$n+1$ instead of an embedding r^~S^n→R^$n+1$ in terms of hedgehogs.
論文 | ランダム
- コンピュ-タ-ソフトウェアについて--コンピュ-タ-プログラムの法的保護をめぐる現状 (知的所有権を考える)
- SF6 retention rate法による肺内シャントの測定-3-洗滌肺における実験的研究
- SF6 retention rate法による肺内シャントの測定-1-正常犬肺における実験的研究
- 開頭術におけるNLAによる低体温麻酔法の臨床的研究 特にhalothane,methoxyfluraneとの比較
- 前方進入路による頸椎カリエス手術経験