Differential Geometry from a Singularity Theory Viewpoint
Differential Geometry from a Singularity Theory Viewpoint
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DOI：
10.1142/9108
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
S. Izumiya;M. Fuster;M. Ruas;F. Tari
中科院分区：
文献类型：
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作者：
S. Izumiya;M. Fuster;M. Ruas;F. Tari
微分几何从奇点理论的观点提供了一个新的视角在迷人的和经典的主题微分几何曲面在欧几里得空间。这本书使用奇点理论来捕捉一些关键的几何特征的表面。它描述了接触理论及其与焦散线和波阵面理论的联系。然后，它使用这些理论的强大的技术来推导嵌入在3，4和5维欧氏空间的表面的几何信息。这本书还包括最近的工作的作者和他们的合作者对几何的子流形在闵可夫斯基空间。
Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.