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Strongly contracting geodesics in Outer Space [PDF]
Geometry & Topology, 2011 We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a quasi-geodesic with endpoints on the axis stays ...
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European Physical Journal C: Particles and FieldsThermodynamic geometry allow us to study the microscopic behavior of black hole system by defining a metric structure in thermodynamic phase space. Among the various thermodynamic metric structures, metrics defined by geometrothermodynamics (GTD) are ...
Gunindra Krishna Mahanta
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The hyperbolicity constant of infinite circulant graphs
Open Mathematics, 2017 If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X.
Rodríguez José M., Sigarreta José M.
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On geodesics in the spaces of constrained curves
Differential Geometry and its ApplicationsIn this work, we study the geodesics of the space of certain geometrically and physically motivated subspaces of the space of immersed curves endowed with a first order Sobolev metric. This includes elastic curves and also an extension of some results on planar concentric circles to surfaces. The work focuses on intrinsic and constructive approaches.
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Approximating the smallest $k$-enclosing geodesic disc in a simple polygon
Journal of Computational GeometryWe consider the problem of finding a geodesic disc of smallest radius containing at least $k$ points from a set of $n$ points in a simple polygon that has $m$ vertices, $r$ of which are reflex vertices. We refer to such a disc as a SKEG disc. We present
Prosenjit Bose +2 more
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On Pseudospherical Smarandache Curves in Minkowski 3-Space
Journal of Applied Mathematics, 2014 In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame’s vectors
Esra Betul Koc Ozturk +3 more
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CEVA, MENELAUS AND STEWART THEOREMS FOR GEODESIC TRIANGLES ON THE HYPERBOLIC UNIT SPHERE
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2009 : In this study, we give Ceva, Menelaus and Stewart Theorems for geodesic triangles on the hyperbolic unit sphere . Keywords: Geodesic triangle, Lorentz space, timelike vector.
Mehmet ÖNDER
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Timelike surfaces with Bertrand geodesic curves in Minkowski 3–space
AIP AdvancesGeodesic curves on a surface play an essential role in reasonable implementation. A curve on a surface is a geodesic curve if its principal normal vector is aligned with the surface normal. Using the Serret–Frenet frame, the timelike (TL) surfaces can be
A. A. Almoneef, R. A. Abdel-Baky
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Recognizing Weighted Means in Geodesic Spaces
Foundations of Computational MathematicsGeodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally whether or not a given point is such an average, exactly or approximately. In nonpositively curved spaces, several
Ariel Goodwin +3 more
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Scientific ReportsThe Alfvén instability nonlinearly excited the energetic-particle-driven geodesic acoustic mode on the ASDEX-Upgrade tokamak, as demonstrated experimentally.
Hao Wang +8 more
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