However, it has a peculiar behavior near y [right arrow] [infinity] (the interior of the geometry) and in fact it is geodesically
Gromov-see, e.g., , page 159) if it is geodesically
connected, and if every geodesic triangle in X is at least as "thin" as its comparison triangle in the Euclidean plane.
Let ([bar.M], [bar.g]) be null geodesically
complete spacetime obeying the null energy condition [bar.Ric](X, X) [greater than or equal to] 0 for all null vectors X such that the hypothesis of Theorem 1 holds.
According to the Penrose-Hawking singularity theorems [22-24], a trapped surface inevitably leads to a geodesically
incomplete spacetime manifold, implying the imminent formation of a singularity.
This database is mainly used by surveyors, who can see the land owners and landmark coordinations of geodesically
measured land plots.
The Hopf-Rinow theorem implies that manifold [S.sup.+] (n) with the Riemannian metric (7) is geodesically
complete ([22, Theorem 2.8]).
In addition, according to the Hopf-Rinow theorem, a compact connected Lie group is geodesically
When the manifold [S.sup.n.sub.+]is endowed with its natural inner product (4.3) (see Section 4.1.2), the cost function f is strictly geodesically
convex, which is a generalization of the classical convexity as follows: let X,Y [member of] [S.sup.n.sub.+], and t [member of] [0,1].
The array of all pairs of geodesies distances allows to segment an image in geodesically
connected regions (i.e., geodesic balls, Noyel et al., 2007b).
Designed as independent projects, some of the key sculptures in EKWC Ceramaskin (specifically a five-foot-long, gray-stoneware ramp geodesically
articulated into facets and an earthenware limb divaricating into smaller branches held together with green electrician's tape and sprouting buds of tiny electrified lights) would be separated at the end of the exhibition, then later physically and conceptually reunited in a 2009 exhibition at the Urban Institute of Contemporary Art in Grand Rapids, Michigan.
A function f: R [right arrow] R is called geodesically