---

＜電子ブック＞
Geometry IV : Non-regular Riemannian Geometry / edited by Yu.G. Reshetnyak
(Encyclopaedia of Mathematical Sciences ; 70)

版	1st ed. 1993.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1993
本文言語	英語
大きさ	VII, 252 p : online resource
冊子体	Non-regular Riemannian geometry / Yu.G. Reshetnyak (ed.) ; : gw,: us
著者標目	Reshetnyak, Yu.G editor SpringerLink (Online service)
件　名	LCSH:Geometry, Differential FREE:Differential Geometry
一般注記	I. Two-Dimensional Manifolds of Bounded Curvature -- II. Multidimensional Generalized Riemannian Spaces -- Author Index 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 such curves. Spaces satisfying this condition are called spaces with intrinsic metric. Next we introduce metric spaces with intrinsic metric satisfying in one form or another the condition that the curvature is bounded Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-662-02897-1

 類似資料