| 書目名稱 | Geometry IV | | 副標(biāo)題 | Non-regular Riemanni | | 編輯 | Yu. G. Reshetnyak | | 視頻video | http://file.papertrans.cn/384/383750/383750.mp4 | | 叢書名稱 | Encyclopaedia of Mathematical Sciences | | 圖書封面 |  | | 描述 | The book contains a survey of research on non-regular Riemannian geome- try, carried out mainly by Soviet authors. The beginning of this direction oc- curred in the works of A. D. Aleksandrov on the intrinsic geometry of convex surfaces. For an arbitrary surface F, as is known, all those concepts that can be defined and facts that can be established by measuring the lengths of curves on the surface relate to intrinsic geometry. In the case considered in differential is defined by specifying its first geometry the intrinsic geometry of a surface fundamental form. If the surface F is non-regular, then instead of this form it is convenient to use the metric PF‘ defined as follows. For arbitrary points X, Y E F, PF(X, Y) is the greatest lower bound of the lengths of curves on the surface F joining the points X and Y. Specification of the metric PF uniquely determines the lengths of curves on the surface, and hence its intrinsic geometry. According to what we have said, the main object of research then appears as a metric space such that any two points of it can be joined by a curve of finite length, and the distance between them is equal to the greatest lower bound of the lengths of su | | 出版日期 | Book 1993 | | 關(guān)鍵詞 | Approximation durch Polyeder; Beschr?nkte Krümmung; Bounded Curvature; Integralkrümmung; K-Konkavit?t; Ma | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-662-02897-1 | | isbn_softcover | 978-3-642-08125-5 | | isbn_ebook | 978-3-662-02897-1Series ISSN 0938-0396 | | issn_series | 0938-0396 | | copyright | Springer-Verlag Berlin Heidelberg 1993 |
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