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Geodesics and Almost Geodesics Curves [PDF]
Results in Mathematics, 2018 We determine in $$\mathbb {R}^n$$ the form of curves $$\mathcal C$$
Olga Belova +2 more
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ACM SIGGRAPH 2010 papers, 2010
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend ...
Pottmann, Helmut +6 more
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Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend ...
Pottmann, Helmut +6 more
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, 1997 In this chapter we study the geodesic vector field on the tangent bundle of the 3-sphere. We examine its relation to the Kepler vector field, which governs the motion of two bodies in R 3 under gravitational attraction. We give two methods to regularize the flow of the Kepler vector field: one energy surface by energy surface and the other for all ...
Larry Bates, Richard Cushman
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Geodesic compatibility and integrability of geodesic flows
Journal of Mathematical Physics, 2003We give a natural geometric condition called geodesic compatibility that implies the existence of integrals in involution of the geodesic flow of a pseudo-Riemannian metric. We prove that if two metrics satisfy the condition of geodesic compatibility then we can produce a hierarchy of metrics that also satisfy this condition. A lot of metrics studed in
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Analysis and Applications, 2003
We consider a subRiemannian geometry induced by a step 3 subelliptic partial differential operator in ℝ3. Our main result is the characterization of a canonical submanifold through the origin, all of whose points are connected to the origin by infinitely many (subRiemannian) geodesics.
Ovidiu Calin, Peter Greiner
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We consider a subRiemannian geometry induced by a step 3 subelliptic partial differential operator in ℝ3. Our main result is the characterization of a canonical submanifold through the origin, all of whose points are connected to the origin by infinitely many (subRiemannian) geodesics.
Ovidiu Calin, Peter Greiner
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Geometriae Dedicata, 1991
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John K. Beem, Phillip E. Parker
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John K. Beem, Phillip E. Parker
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Geodesic as Limit of Geodesics on PL-Surfaces
2008We study the problem of convergence of geodesics on PL-surfaces and in particular on subdivision surfaces. More precisely, if a sequence (Tn)n∈N of PL-surfaces converges in distance and in normals to a smooth surface S and if Cn is a geodesic of Tn (i.e.
André Lieutier, Boris Thibert
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Hamilton–Jacobi formalism for geodesics and geodesic deviations
Journal of Mathematical Physics, 1989A formalism of integrating the equations of geodesics and of geodesic deviation is examined based upon the Hamilton–Jacobi equation for geodesics. The latter equation has been extended to the case of geodesic deviation and theorems analogous to Jacobi’s theorem on the complete integral has been proved.
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Journal of Graph Theory, 1983
AbstractDefine a geodesic subgraph of a graph to be a subgraph H with the property that any geodesic of two points of H is in H. The trivial geodesic subgraphs are the complete graphs Kn' n ≧ 0, and G itself. We characterize all (finite, simple, connected) graphs with only the trivial geodesic subgraphs, and give an algorithm for their construction. We
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AbstractDefine a geodesic subgraph of a graph to be a subgraph H with the property that any geodesic of two points of H is in H. The trivial geodesic subgraphs are the complete graphs Kn' n ≧ 0, and G itself. We characterize all (finite, simple, connected) graphs with only the trivial geodesic subgraphs, and give an algorithm for their construction. We
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1998
We are now ready to move on to the local and global geometry of Riemannian manifolds. The main tool for this will be the important concept of geodesics. These curves will help us define and understand Riemannian manifolds as metric spaces. One is led quickly to two types of “completeness”.
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We are now ready to move on to the local and global geometry of Riemannian manifolds. The main tool for this will be the important concept of geodesics. These curves will help us define and understand Riemannian manifolds as metric spaces. One is led quickly to two types of “completeness”.
openaire +2 more sources