| 书目名称 | Lectures on Spaces of Nonpositive Curvature | | 编辑 | Werner Ballmann | | 视频video | | | 丛书名称 | Oberwolfach Seminars | | 图书封面 |  | | 描述 | Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifo | | 出版日期 | Book 1995 | | 关键词 | Group theory; Riemannian manifold; curvature; differential equation; foliation; manifold; set | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-9240-7 | | isbn_softcover | 978-3-7643-5242-4 | | isbn_ebook | 978-3-0348-9240-7Series ISSN 1661-237X Series E-ISSN 2296-5041 | | issn_series | 1661-237X | | copyright | Birkhäuser Verlag 1995 |
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发表于 2025-3-21 18:15:31
