| 释义 |
Riemannian, a. Math.|riːˈmænɪən|
[f. as prec. + -ian.]
Used to designate a non-Euclidean geometry which is everywhere positively curved, and various associated concepts.
1920A. S. Eddington Space, Time & Gravitation xii. 183 The world became non-Euclidean; a new geometry called Riemannian geometry was adopted. 1923Ann. Math. XXIV. 367 A generalization of Levi-Civita's concept of infinitesimal parallelism in a Riemannian manifold. 1926L. P. Eisenhart Riemannian Geom. ii. 35 The metric defined..is called the Riemannian metric and a geometry based upon such a metric is called a Riemannian geometry. Also we say that the space whose geometry is based upon such a metric is called a Riemannian space. 1965H. Eves Survey of Geom. II. xiv. 341 One can describe Riemannian geometry as the mathematical study, couched in geometrical terminology, of an arbitrary quadratic differential form. 1974Encycl. Brit. Micropædia VIII. 580/2 In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same length. |