| 書目名稱 | Geometries and Groups | | 編輯 | Viacheslav V. Nikulin,Igor R. Shafarevich | | 視頻video | http://file.papertrans.cn/384/383703/383703.mp4 | | 叢書名稱 | Universitext | | 圖書封面 |  | | 描述 | This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of the Euclidean plane or 3-space; we also consider the relation between discrete groups of motions and crystallography. The description of locally Euclidean geometries of one type shows that these geometries are themselves naturally represented as the points of a new geometry. The systematic study of this new geometry leads us to 2-dimensional Lobachevsky geometry (also called non-Euclidean or hyperbolic geometry) which, following the logic of our study, is constructed starting from the properties of its group of motions. Thus in this book we would like to introduce the reader to a theory of geometries which are different from the usual Euclidean geometry of the plane and 3-space, in terms of examples which are accessible to a concrete and intuitive study. The basic method of study is the use of groups of motions, both discrete groups and the | | 出版日期 | Textbook 1994 | | 關(guān)鍵詞 | Lattice; Mathematica; Non-Euclidean Geometry; Symmetry group; addition; algebra; boundary element method; f | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-61570-2 | | isbn_softcover | 978-3-540-15281-1 | | isbn_ebook | 978-3-642-61570-2Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | Springer-Verlag Berlin Heidelberg 1994 |
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