WEAKLY IRREGULAR SURFACES OF NEGATIVE CURVATURE
WEAKLY IRREGULAR SURFACES OF NEGATIVE CURVATURE
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负曲率弱不规则曲面
DOI：
10.1070/rm1966v021n05abeh004174
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发表时间：
1966
影响因子：
0.9
通讯作者：
Ė. R. Rozendorn
中科院分区：
文献类型：
--
作者：
Ė. R. Rozendorn
第一章.弱不规则点的邻域§ 1。鞍形曲面，外曲率和内曲率§ 2.渐近线§ 3.内禀度量对鞍阶的影响§ 4.内在度量对渐近网结构的影响§ 5.有界平均曲率的情形第2章.弱不规则曲面的局部构造方法§ 6.一个弱不规则嵌入E3的一个分析度量的负曲率§ 7。在渐近线的行为的特殊性§ 8。具有可微负高斯曲率的m ≥ 3阶鞍点第三章. E3和E4 § 9中负曲率的完整曲面。定理C的证明§ 10。“熨平”一个平面鞍型山脊，保留K § 11的标志。E ~ 3中曲率K ≤ -1 § 12的完备弱不规则曲面。E4 Supplement中的一个负曲率闭正则曲面。一些未解决的问题参考文献
CONTENTSIntroductionChapter 1. The neighbourhood of a weakly irregular point § 1. Saddle surfaces, extrinsic and intrinsic curvature § 2. Asymptotic lines § 3. The influence of the intrinsic metric on the order of a saddle § 4. The influence of the intrinsic metric on the structure of the asymptotic net § 5. The case of bounded mean curvatureChapter 2. Methods for the local construction of weakly irregular surfaces § 6. A weakly irregular embedding in E3 of an analytic metric of negative curvature § 7. Peculiarities in the behaviour of the asymptotic lines § 8. A saddle of order m ≥ 3 with differentiable negative Gaussian curvatureChapter 3. Complete surfaces of negative curvature in E3 and E4 § 9. Proof of Theorem C § 10. "Ironing out" a plane saddle-type ridge with preservation of the sign of K § 11. A complete weakly irregular surface in E3 with curvature K ≤ –1 § 12. A closed regular surface of negative curvature in E4Supplement. Some unsolved problemsReferences