Assertion: euclidean space | /r/HasProperty | flat
Facets:
value: globally
type: DEGREE
value: conformally
type: MANNER
value: in this sense
type: OTHER
Source sentences:
text: For example, Euclidean space is flat, simply connected, and infinite, but the torus is flat, multiply connected, finite, and compact.
text: Nevertheless, since Bernhard Riemann (1826-1866), non-Euclidean manifolds are said to be "curved," and only Euclidean space itself is called "flat.
text: A pseudo-Euclidean space is flat, that is, its Riemann tensor is zero.
text: Euclidean space, and Euclidean geometry by extension, is assumed to be flat and non-curved.
text: Euclidean space, and Euclidean geometry by extension, is assumed to be flat and non-curved.
text: The n-sphere is a locally conformally flat manifold that is not globally conformally flat in this sense, whereas a Euclidean space, a torus, or any conformal manifold that is covered by an open subset of Euclidean space is (globally) conformally flat in this sense.