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Geodesic Torsions and Geodesic Curvatures in Riemannian Spaces

Geodesic Torsions and Geodesic Curvatures in Riemannian Spaces
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The orbitofrontal cortex forms a context-generalized spatial schema that preserves topology and distance

Basu R, Mozaffarilegha M, Bölükbaşı I, Üstüner C, Ito HT.   +4 more
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Geodesics in Weakly Symmetric Spaces

Annals of Global Analysis and Geometry, 1997
A Riemannian manifold \(M\) is said to be weakly symmetric if for every two points \(p\) and \(q\) in \(M\) there is an isometry of \(M\) interchanging \(p\) and \(q\). The authors prove that every geodesic in a weakly symmetric space is an orbit of a one-parameter group of isometries of \(M\).
Berndt, Jürgen, Kowalski, Oldřich, Vanhecke, Lieven   +2 more
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Branching geodesics in normed spaces

Izvestiya: Mathematics, 2002
Summary: We study branching extremals of length functionals on normed spaces. This is a natural generalization of the Steiner problem in normed spaces. We obtain criteria for a network to be extremal under deformations that preserve the topology of networks as well as under deformations with splitting. We discuss the connection between locally shortest
Ivanov, A. O., Tuzhilin, A. A.
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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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