On the geometric results of A. V. Pogorelov

被引:0
作者
Aminov Yu.A. [1 ]
机构
[1] Institute for Low-Temperature Physics and Engineering, Ukrainian National Academy of Sciences, Kharkov
关键词
Gaussian Curvature; Convex Surface; Riemannian Space; Isometric Immersion; Finsler Space;
D O I
10.1007/s11253-007-0083-3
中图分类号
学科分类号
摘要
We present a survey of the principal results of A. V. Pogorelov in the field of geometry. © 2007 Springer Science+Business Media, Inc.
引用
收藏
页码:1238 / 1252
页数:14
相关论文
共 37 条
[1]  
Reports of the International Seminar on Geometry "in the Large" Dedicated to the 85th Anniversary of Academician A. V. Pogorelov
[2]  
Aleksandrov A.V., On one class of closed surfaces, Mat. Sb., 4, pp. 69-77, (1938)
[3]  
Pogorelov A.V., Unique definition of general convex surfaces, Dokl. Akad. Nauk SSSR, 79, pp. 739-742, (1951)
[4]  
Gayubov G.N., Unique definition of surfaces in the Lobachevskii space, Nauch. Trudy Tashkent Univ., 394, pp. 52-62, (1970)
[5]  
Danelich I.A., Unique definition of some convex surfaces in the Lobachevskii space, Dokl. Akad. Nauk SSSR, 115, pp. 217-219, (1957)
[6]  
Milka A.D., Unique definition of general convex surfaces in the Lobachevskii space, Ukr. Geom. Sborn., 23, pp. 99-107, (1980)
[7]  
Pogorelov A.V., Extrinsic Geometry of Convex Surfaces, (1969)
[8]  
Gromov M.L., Rokhlin V.A., Imbeddings and immersions in the Riemannian geometry, Usp. Mat. Nauk, 25, pp. 3-62, (1970)
[9]  
Pogorelov A.V., An example of a two-dimensional Riemannian metric that does not admit local realizations in e <sup>3</sup>, Dokl. Akad. Nauk SSSR, 198, pp. 42-43, (1971)
[10]  
Fomenko V.T., On the rigid and unique definition of closed surfaces of kind p ≥ 1 in the Riemannian space, Dokl. Akad. Nauk SSSR, 213, pp. 45-50, (1973)