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On a Class of Geodesics in Teichmuller Space
The Annals of Mathematics, 1975The study of the geometry of the classical Teichmiiller spaces was begun in 1959 by Kravetz [9]. The starting point was the classical theorem of TeichmUller on extremal quasiconformal maps between compact Riemann surfaces. The TeichmUller theorem was used to argue that with respect to the Teichmiiller metric, TeichmUller space is straight and that it ...
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On Geodesics in Euclidean Shape Spaces
Journal of the London Mathematical Society, 1991The 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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Generalised geodesics in a Riemannian space
Bulletin de la Classe des sciences, 1967Asymptotic lines of order p have been defined by Hayden in [1]. In this paper we define geodesies of order p, investigate their properties and establish their relationship with the asymptotic lines of order p.
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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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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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On the Electromagnetic Geodesic in Space
We present a field-theoretic framework for modeling electromagnetic energy propagation in heterogeneous media by introducing the concept of electromagnetic geodesics. Unlike traditional ray optics, which assumes either a straight-line propagation or a simple bending in refractive media, our approach formulates wave propagation as geodetic motion in a ...Jacob T Fokkema, Peter M van den berg
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Geodesic Orbit Spaces of Compact Lie Groups of Rank Two
Geometriae Dedicata, 2022Nikolaos Panagiotis Souris
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On the Structure of Geodesic Orbit Riemannian Spaces
Annals of Global Analysis and Geometry, 2017Yury Nikonorov
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The Shape Space of Discrete Orthogonal Geodesic Nets
ACM Transactions on Graphics, 2018Olga Sorkine-Hornung
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The Space of Null Geodesics (and a New Causal Boundary)
Lecture Notes in Physics, 2006Robert J Low
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