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View from inside
http://hdl.handle.net/10131/7888
http://hdl.handle.net/10131/78889254d0ba-698d-4de3-8242-e8ac9de16f4e
名前 / ファイル | ライセンス | アクション |
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12.pdf (1.1 MB)
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2012-03-15 | |||||
タイトル | ||||||
タイトル | View from inside | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | perspective projection, perspective point, projective dual, dual hypersurface, hedgehog | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | journal article | |||||
著者 |
Nishimura, Takashi
× Nishimura, Takashi× Sakemi, Yu |
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著者(ヨミ) | ||||||
識別子Scheme | WEKO | |||||
識別子 | 217 | |||||
識別子Scheme | e-Rad | |||||
識別子URI | https://kaken.nii.ac.jp/ja/search/?qm= 80189307 | |||||
識別子 | 80189307 | |||||
姓名 | ニシムラ, タカシ | |||||
著者(ヨミ) | ||||||
識別子Scheme | WEKO | |||||
識別子 | 22147 | |||||
姓名 | サケミ, ユウ | |||||
著者別名 | ||||||
識別子Scheme | WEKO | |||||
識別子 | 217 | |||||
識別子Scheme | e-Rad | |||||
識別子URI | https://kaken.nii.ac.jp/ja/search/?qm= 80189307 | |||||
識別子 | 80189307 | |||||
姓名 | 西村, 尚史 | |||||
著者所属 | ||||||
Research Group of Mathematical Sciences Research Institute of Environment and Information Sciences Yokohama National University | ||||||
著者所属 | ||||||
NTT COMWARE | ||||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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. | |||||
書誌情報 |
Hokkaido Mathematical Journal 巻 40, 号 3, p. 361-373, 発行日 2011-10 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 03854035 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00664662 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
出版者 | ||||||
出版者 | Department of Mathematics, Hokkaido University |