Geodesics and Curvature
Examples of spaces with branching geodesics satisfying the curvature-dimension condition
... that geodesics still can branch in this kind of essentially non-branching ...Riemannian curvature-dimension condition RCD(K, ∞) introduced by Ambrosio, Gigli and Savar´ e ...
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CURVATURE, GEODESICS AND THE BROWNIAN MOTION ON A RIEMANNIAN MANIFOLD II
... This paper may be considered to be a continuation, in which the relation between explosions of the Brownian motion X and geodesies, curvature of the Riemannian manifold M will be investi[r] ...
Geodesics of surface of revolution
... Geodesic Curvature Figure 5.1: Normal and Geodesic Curvature Let C : X(s) (s is arc length) is a curve on surface S, then X is a unit vector and a tangent vector to ...
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Computing Geodesics on Triangular Meshes ⋆
... (3) γ is parallel to the surface normal. (4) γ has vanishing geodesic curvature κ g = 0 1 . From item 4 of proposition 3 above, it can be concluded that geodesic curves are as straight as they can be, if we see ...
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Pairs of closed geodesics in metric graphs
... closed geodesics in surfaces of negative curvature due to the fact that the coding of metric graphs we use results in a subshift of finite type, just as in the analysis of pairs of closed geodesics ...
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Focal curves of geodesics on generalized cylinders
... non-planar geodesics on the right generalized cylinder are ...The curvature and torsion of the geodesic and its focal curve are expressed in terms of the signed curvature of the above-mentioned plane ...
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Asymptotic expansion of closed geodesics in homology classes
... (T, α) = π (T, α). However, e − hT 1 / 4N + b + 3 → 0 faster than 1 / T n for any n. So we have the following theorem. T HEOREM 2. Let M be a compact Riemannian manifold with first Betti number b > 0 and with negative ...
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Principal component geodesics for planar shape spaces
... The statistical study of geometrical shapes by extracting finite landmark configurations and mapping to metric quotient- spaces was independently triggered by Bookstein [ 1 ], Kendall [ 2 ] and Ziezold [ 3 ]. Different ...
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and curvature measures
... and curvature measures Alan ...of geodesics normal to M passing through ...of curvature measures of M ...constant curvature −K. If we average number of geodesics normal to M passing ...
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Three Dimensional Manifolds All of Whose Geodesics Are Closed
... homeomorphic to S 2 . Consider the principal bundle S 1 → N → S 2 , with projection q . We want to conclude that the Euler class of this bundle is nonzero. First note that the geodesic vector eld is tangent to the xed ...
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Quasi-Hyperbolic Geodesics are Hyperbolic Quasi-Geodesics
... e τ ≤ e r ≤ 2e 4σ−s + e 2σ−r ≤ e 2σ−τ (2e 2σ + 1) but then e 4σ ≤ e 2τ −2σ ≤ 2e 2σ + 1 which contradicts σ > log 6. 4. Length Estimates Below we provide explicit estimates for the Euclidean, hyperbolic, and ...
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GEODESICS IN LORENTZIAN MANIFOLDS
... Chapter 1 Introduction A geodesic on a Riemannian manifold is, locally, a length minimizing curve. In other words, a geodesic is a path that a non-accelerating particle would follow. For example, a geodesic in the ...
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Geodesics of ruled surfaces
... Ramirez, Steven John, "Geodesics of ruled surfaces" (2001). Theses Digitization Project. 2020. https://scholarworks.lib.csusb.edu/etd-project/2020 This Thesis is brought to you for free and open access by the John ...
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Geodesics and flows in a Poissonian city
... Three dimensions and higher In higher dimensions one needs to consider what kind of network is being deployed. One might for example consider the edge process of a Poisson hyperplane tessellation, or alternatively one ...
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1.1 Minkowski space and geodesics
... Holmes-Thompson areas Yang Liu Abstract. In this article, we mainly study the Holmes-Thompson areas in Minkowski space. The space of geodesics in Minkowski space has a symplectic structure which is induced by the ...
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Kruskal Dynamics for Radial Geodesics
... The total spacetime manifold for a Schwarzschild black hole (BH) is believed to be described by the Kruskal coordi- nates and , where r and t are the conventional Schwarzschild ra[r] ...
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Fast Exact Geodesics on Meshes
... Exact Geodesics Algorithm presented by Mitchell, Mount, and Pa- padimitriou (MMP) on triangular meshes, for which an implementation is described in the paper by Surazhsky et ...
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Geodesics and flows in a Poissonian city
... University of Warwick The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1–21]. The current paper ...
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Homogeneous geodesics and g.o. manifolds
... whose geodesics are homogeneous is called a pseudo-Riemannian ...spaces, geodesics are homogeneous in almost all directions, but there is a singular set of directions, in which geodesics are not ...
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Geodesics on Generalized Plane Wave Manifolds
... 5.2 Geodesics We will begin by describing the intuitive nature of geodesics on ...all geodesics are great circles. We can speak of geodesics in this intuitive sense on Riemannian manifolds ...
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