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...It may be formalized as the projection of a closed orbit of the [[geodesic|geodesic flow]] on the [[tangent space]] of the manifold. ...geodesic is a curve <math>\gamma:\mathbb R\rightarrow M</math> that is a [[geodesic]] for the metric ''g'' and is periodic. ...

...</ref> By imposing a weak global [[non-positive curvature]] condition on a geodesic bicombing several results from the theory of [[CAT(k) space|CAT(0) spaces]] ...ast1=Descombes|first1=Dominic|last2=Lang|first2=Urs|date=2015|title=Convex geodesic bicombings and hyperbolicity|journal=[[Geometriae Dedicata]]|language=en|vo ...

...description|Gives the Gaussian curvature of a surface from the length of a geodesic circle or its area}} ...terms of the [[circumference]] of a [[geodesic]] circle, or the area of a geodesic disc. The theorem is named for [[Joseph Bertrand]], [[Victor Puiseux]], an ...

...nnection#Geodesics and the absorption of torsion|affinely parametrized]] [[geodesic]]s. The method is named for [[Alfred Schild]], who introduced the method d ...a is to identify a tangent vector ''x'' at a point <math>A_0</math> with a geodesic segment of unit length <math>A_0X_0</math>, and to construct an approximate ...

In the [[mathematics|mathematical]] field of [[differential geometry]], the '''Levi-Civita paral ...o or the same length as the side ''AB,'' although it will be straight (a [[geodesic]]).<ref>In the article by Levi-Civita (1917, p. 199), the segments AB and A ...

In the [[mathematics|mathematical]] field of [[Riemannian geometry]], '''Toponogov's theorem''' ...ngle]], i.e. a triangle whose sides are geodesics, in ''M'', such that the geodesic ''pq'' is minimal and if &delta; > ''0'', the length of the side ''pr'' is ...

...eometry With Applications to Relativity|volume=103|series=Pure and Applied Mathematics|first=Barrett|last=O'Neill|publisher=[[Academic Press]]|year=1983|isbn=9780 ...ath>. Then <math>\Gamma</math> has a proper, discontinuous [[Group action (mathematics)|action]] on <math>M</math>. Hence the quotient <math>T = M/\Gamma,</math> ...

In [[mathematics]], a '''Busemann ''G''-space''' is a type of [[metric space]] first describ ...nus\{ x,y \} )^\circ</math> such that <math>d(x,y)+d(y,z)=d(x,z)</math> ([[geodesic]]s are locally extendable) ...

In mathematics, the '''Gromov boundary''' of a [[δ-hyperbolic space]] (especially a [[hype ...of the most common uses equivalence classes of [[geodesic#Metric geometry|geodesic]] rays.<ref>{{harvnb|Kapovich|Benakli|2002}}</ref> ...

In [[mathematics]], the '''Cartan–Ambrose–Hicks theorem''' is a theorem of [[Riemannian geom ...ttps://projecteuclid.org/euclid.ijm/1255455125|journal=Illinois Journal of Mathematics|volume=3|issue=2|pages=242–254|doi=10.1215/ijm/1255455125|issn=0019-2082|do ...

In [[mathematics]], the '''Tits metric''' is a [[metric (mathematics)|metric]] defined on the ideal boundary of an [[Hadamard space]] (also call Let (''X'', ''d'') be an Hadamard space. Two [[geodesic]] rays ''c''₁, ''c''₂ : [0, ∞] → ''X'' are called ''' ...

| image1 = Geodesic icosahedral polyhedron_example.png | image2 = Geodesic icosahedral polyhedron_example2.png ...

...lding blocks other geometric objects, belonging to a well defined [[Class (mathematics)|class]]. Intuitively, it states that a [[manifold]] obtained by joining (i ...ete metric space|complete]] [[locally compact]] [[Geodesic#Metric geometry|geodesic]] [[metric space]]s of [[CAT(k) space|CAT curvature]] <math>\leq \kappa</ma ...

...e bundle]] of a [[Riemannian manifold]] by first integrating along every [[geodesic]] separately and then ...rall s\in [0,t]:~ \varphi_s(x,v)\in SM \} </math> is the exit time of the geodesic with initial conditions <math> (x,v)\in SM </math>, ...

...and the Björling's problem. MIT BA Thesis. 2004 http://ocw.mit.edu/courses/mathematics/18-994-seminar-in-geometry-fall-2004/projects/main1.pdf</ref> ...be a symmetry plane of the surface.<ref>Björling problem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bj%C3%B6rling_probl ...

...h]]s of each other. A Goldberg polyhedron is a [[dual polyhedron]] of a [[geodesic polyhedron]]. ||[[List of geodesic polyhedra and Goldberg polyhedra#Icosahedral|more]] ...

...hen its volume entropy coincides with the [[topological entropy]] of the [[geodesic flow]]. It is of considerable interest in differential geometry to find the ...ntered at <math>\tilde{x}_0</math> and ''vol'' is the Riemannian [[volume (mathematics)|volume]] in the universal cover with the natural Riemannian metric. ...

...] is a [[Net (polyhedron)|net]] obtained by cutting the polyhedron along [[geodesic]]s (shortest paths) through its faces. It has also been called the '''inwar ...P</math>, in [[general position]], meaning that there is a unique shortest geodesic from <math>p</math> to each [[Vertex (geometry)|vertex]] of <math>P</math>. ...

{{Short description|Integral transform type in mathematics}} In [[mathematics]], an '''orbital integral''' is an [[integral transform]] that generalizes ...

...ra and Goldberg polyhedra are [[polyhedral dual|duals]] of each other. The geodesic and Goldberg polyhedra are parameterized by integers ''m'' and ''n'', with ! rowspan=2 | Vertices<br>(geodesic)<br>Faces<br>(Goldberg) ...