. . . . . . . . . "In mathematics, a smooth compact manifold M is called almost flat if for any there is a Riemannian metric on M such that and is -flat, i.e. for the sectional curvature of we have . Given n, there is a positive number such that if an n-dimensional manifold admits an -flat metric with diameter then it is almost flat. On the other hand, one can fix the bound of sectional curvature and get the diameter going to zero, so the almost-flat manifold is a special case of a collapsing manifold, which is collapsing along all directions."@en . . . "\u041F\u043E\u0447\u0442\u0438 \u043F\u043B\u043E\u0441\u043A\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u2014 \u0433\u043B\u0430\u0434\u043A\u043E\u0435 \u043A\u043E\u043C\u043F\u0430\u043A\u0442\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u041C \u0442\u0430\u043A\u043E\u0435, \u0447\u0442\u043E \u0434\u043B\u044F \u043B\u044E\u0431\u043E\u0433\u043E \u043D\u0430 \u041C \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0438\u043C\u0430\u043D\u043E\u0432\u0430 \u043C\u0435\u0442\u0440\u0438\u043A\u0430 ,\u0442\u0430\u043A\u0430\u044F, \u0447\u0442\u043E \u0438 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F -\u043F\u043B\u043E\u0441\u043A\u043E\u0439,\u0442\u043E \u0435\u0441\u0442\u044C \u0435\u0451 \u0441\u0435\u043A\u0446\u0438\u043E\u043D\u043D\u044B\u0435 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u044B \u0432 \u043A\u0430\u0436\u0434\u043E\u0439 \u0442\u043E\u0447\u043A\u0435 \u0443\u0434\u043E\u0432\u043B\u0435\u0442\u0432\u043E\u0440\u044F\u044E\u0442 \u043D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u0443"@ru . . . . . . . . . . . . . "2715"^^ . . . . . . . . . . . . "Inom matematiken s\u00E4ges en kompakt m\u00E5ngfald M vara n\u00E4stan platt om f\u00F6r varje finns det en p\u00E5 M s\u00E5 att och \u00E4r -platt, d.v.s. vi har olikheten f\u00F6r av ."@sv . "\u041F\u043E\u0447\u0442\u0438 \u043F\u043B\u043E\u0441\u043A\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435"@ru . "In mathematics, a smooth compact manifold M is called almost flat if for any there is a Riemannian metric on M such that and is -flat, i.e. for the sectional curvature of we have . Given n, there is a positive number such that if an n-dimensional manifold admits an -flat metric with diameter then it is almost flat. On the other hand, one can fix the bound of sectional curvature and get the diameter going to zero, so the almost-flat manifold is a special case of a collapsing manifold, which is collapsing along all directions. According to the Gromov\u2013Ruh theorem, M is almost flat if and only if it is infranil. In particular, it is a finite factor of a nilmanifold, which is the total space of a principal torus bundle over a principal torus bundle over a torus."@en . . "\u041F\u043E\u0447\u0442\u0438 \u043F\u043B\u043E\u0441\u043A\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u2014 \u0433\u043B\u0430\u0434\u043A\u043E\u0435 \u043A\u043E\u043C\u043F\u0430\u043A\u0442\u043D\u043E\u0435 \u043C\u043D\u043E\u0433\u043E\u043E\u0431\u0440\u0430\u0437\u0438\u0435 \u041C \u0442\u0430\u043A\u043E\u0435, \u0447\u0442\u043E \u0434\u043B\u044F \u043B\u044E\u0431\u043E\u0433\u043E \u043D\u0430 \u041C \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u0438\u043C\u0430\u043D\u043E\u0432\u0430 \u043C\u0435\u0442\u0440\u0438\u043A\u0430 ,\u0442\u0430\u043A\u0430\u044F, \u0447\u0442\u043E \u0438 \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F -\u043F\u043B\u043E\u0441\u043A\u043E\u0439,\u0442\u043E \u0435\u0441\u0442\u044C \u0435\u0451 \u0441\u0435\u043A\u0446\u0438\u043E\u043D\u043D\u044B\u0435 \u043A\u0440\u0438\u0432\u0438\u0437\u043D\u044B \u0432 \u043A\u0430\u0436\u0434\u043E\u0439 \u0442\u043E\u0447\u043A\u0435 \u0443\u0434\u043E\u0432\u043B\u0435\u0442\u0432\u043E\u0440\u044F\u044E\u0442 \u043D\u0435\u0440\u0430\u0432\u0435\u043D\u0441\u0442\u0432\u0443"@ru . . "Almost flat manifold"@en . . "N\u00E4stan platt m\u00E5ngfald"@sv . "Inom matematiken s\u00E4ges en kompakt m\u00E5ngfald M vara n\u00E4stan platt om f\u00F6r varje finns det en p\u00E5 M s\u00E5 att och \u00E4r -platt, d.v.s. vi har olikheten f\u00F6r av ."@sv . . . "1083533968"^^ . . . . "933946"^^ . . . .