Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1311-9208-1 |
Объём: | 108 страниц |
Масса: | 184 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! In Riemannian geometry, the sphere theorem, also known as the quarter-pinched sphere theorem, strongly restricts the topology of manifolds admitting metrics with a particular curvature bound. The precise statement of the theorem is as follows. If M is a complete, simply-connected, n-dimensional Riemannian manifold with sectional curvature taking values in the interval (1,4] then M is homeomorphic to the n-sphere. (To be precise, we mean the sectional curvature of every tangent 2-plane at each point must lie in (1,4].) Another way of stating the result is that if M is not homeomorphic to the sphere, then it is impossible to put a metric on M with quarter-pinched curvature.
Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.