Results 291 to 300 of about 116,829 (327)

The space of geodesics

Geometriae Dedicata, 1991
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Beem, John K., Parker, Phillip E.
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Integrable geodesic flows on homogeneous spaces

Sbornik: Mathematics, 2001
Consider a compact Lie group \(G\) endowed with a bi-invariant metric, a closed subgroup \(H\), and the homogeneous space \(M= G/H\), endowed with its geodesic flow \(O\). Let \(f_1,\dots, f_\ell\) be a basis of \(O\)-invariant real functions on \(T^1M\). For \(x\in M\), consider the subspace \(F_x\) of \(T^*_x M\) spanned by \(df_1(x),\dots, df_\ell(x)
Bolsinov, A. V., Jovanovič, Božidar Žarko   +1 more
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Geodesics on loop spaces

Journal of Geometry and Physics, 1993
The space of smooth embedded loops \(E(S^ 1,M) \subset C^ \infty(S^ 1,M)\) in a Riemannian manifold \((M,g)\) carries a (weak) Riemannian metric \[ G(\gamma)(s_ 1,s_ 2) = \int_{S^ 1} g(s_ 1(t),s_ 2(t))\text{vol}(\gamma^* g)(t), \] where \(s_ i \in T_ \gamma C^ \infty(S^ 1,M)\) `is' the space of all vector fields along \(\gamma\), which is invariant ...
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Geodesic graphs in Randers g.o. spaces

Commentationes Mathematicae Universitatis Carolinae, 2020
Geodetic graphs were recently studied for Riemannian manifolds. The author generalizes the concept of geodetic graphs to Finsler geometry, in particular to homogeneous Randers g.o. manifolds. On modified H-type groups which admit a Riemannian g.o. metric, invariant Randers g.o. metrics are determined. Geodesic graphs in these Finsler g.o. manifolds are
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Geodesic spaces tangent to metric spaces

Ukrainian Mathematical Journal, 2013
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Geodesic Video Stabilization in Transformation Space

IEEE Transactions on Image Processing, 2017
We present a novel formulation of video stabilization in the space of geometric transformations. With the setting of the Riemannian metric, the optimized smooth path is cast as the geodesics on the Lie group embedded in transformation space. While solving the geodesics has a closed-form expression in a certain space, path smoothing can be easily ...
Lei Zhang, Xiao-Quan Chen, Xin-Yi Kong, Hua Huang   +3 more
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The Monge Problem in Geodesic Spaces

2011
We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish non branching geodesic space. We show that we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce an assumption on the transport problem π which implies that the conditional probabilities of the first marginal on ...
S. Bianchini, F. Cavalletti
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On Geodesics in Euclidean Shape Spaces

Journal of the London Mathematical Society, 1991
The geometry of the shape spaces \(\Sigma_ m^ k\) has been developed in [\textit{D. G. Kendall}, Bull. Lond. Math. Soc. 16, 81-121 (1984; Zbl 0579.62100); \textit{T.K. Carne}, Proc. Lond. Math. Soc., III. Ser. 61, No. 2, 407-432 (1990; Zbl 0723.60014)] and in a recent joint paper of the author and D. Kendall.
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Geodesic Flows on Symmetric Riemann Spaces

The Annals of Mathematics, 1957
Let G be a connected non-compact semi-simple Lie group whose center is finite and K a maximal compact subgroup of G. We denote by G/K the homogeneous space of cosets gK, g e G. Then G/K is a real analytic manifold with the natural analytic structure of a homogeneous space.
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The biofilm matrix: multitasking in a shared space

Nature Reviews Microbiology, 2022
Hans-Curt Flemming, Eric D Van Hullebusch, Thomas R Neu   +2 more
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