Results 21 to 30 of about 264 (216)
On the Hausdorff Dimension of CAT(κ) Surfaces
Analysis and Geometry in Metric Spaces, 2016 We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls.
Constantine David, Lafont Jean-François
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Closed simple geodesics on a polyhedron
, 2023 Abstract It is well-known that every isosceles tetrahedron (disphenoid) admits infinitely many simple closed geodesics on its surface. They can be naturally enumerated by pairs of coprime integers n > m > 1 with two additional cases (1, 0) and (1, 1).
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Mathematics, 2021 In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces.
Volodymyr Berezovski +3 more
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GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES
Forum of Mathematics, Sigma, 2014 We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data as well as for ...
MARTINS BRUVERIS +2 more
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On the determination of shifting operators along geodesics on a surface [PDF]
Theoretical and Applied Mechanics, 2013 A procedure to obtain a closed form of the shifting operators along a known geodesic line on a surface as a solution of a system of linear algebraic equations is proposed.
Drašković Zoran
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Unduloids and their Closed Geodesics
, 2012 We construct explicit parametrizations in terms of elliptic functions for unduloids depending on a parameter. We then use these parametrizations to study geodesics on unduloids. In particular, we use Maple to find interesting closed geodesics on unduloids.
Mladenov, Ivaïlo, Oprea, John
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Mathematics, 2020 In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, and m- (Ricci-)
Volodymyr Berezovski +3 more
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Stability of closed timelike geodesics
Physics Letters A, 2007 5 pages, REvTex, discussion added.
Rosa, V. M., Letelier, P. S.
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Simple Closed Quasigeodesics on Tetrahedra
Information, 2022 Pogorelov proved in 1949 that every convex polyhedron has at least three simple closed quasigeodesics. Whereas a geodesic has exactly a π surface angle to either side at each point, a quasigeodesic has at most a π surface angle to either side at each ...
Joseph O’Rourke, Costin Vîlcu
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A Geodesic-Based Riemannian Gradient Approach to Averaging on the Lorentz Group
Entropy, 2017 In this paper, we propose an efficient algorithm to solve the averaging problem on the Lorentz group O ( n , k ) . Firstly, we introduce the geometric structures of O ( n , k ) endowed with a Riemannian metric where geodesic could be ...
Jing Wang, Huafei Sun, Didong Li
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