Results 41 to 50 of about 3,863,707 (192)
No periodic geodesics in jet space
Pacific Journal of Mathematics, 2023 The $J^k$ space of $k$-jets of a real function of one real variable $x$ admits the structure of a sub-Riemannian manifold, which then has an associated Hamiltonian geodesic flow, and it is integrable. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does $J^k$ have periodic geodesics?
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Riemannian M-spaces with homogeneous geodesics [PDF]
Annals of Global Analysis and Geometry, 2018 We investigate homogeneous geodesics in a class of homogeneous spaces called $M$-spaces, which are defined as follows. Let $G/K$ be a generalized flag manifold with $K=C(S)=S\times K_1$, where $S$ is a torus in a compact simple Lie group $G$ and $K_1$ is the semisimple part of $K$.
Arvanitoyeorgos, Andreas +2 more
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Spaces of geodesics: products, coverings, connectedness [PDF]
Geometriae Dedicata, 1996 We continue our study of the space of geodesics of a manifold with linear connection. We obtain sufficient conditions for a product to have a space of geodesics which is a manifold. We investigate the relationship of the space of geodesics of a covering manifold to that of the base space.
Beem, John K. +2 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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Moduli Spaces of Lumps on Real Projective Space [PDF]
, 2015 Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement.
Muhamed, Abera A +3 more
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Geodesically equivalent metrics on homogenous spaces [PDF]
Czechoslovak Mathematical Journal, 2018 Two metrics on a manifold are geodesically equivalent if sets of their unparameterized geodesics coincide. In this paper we show that if two left $G$-invariant metrics of arbitrary signature on homogenous space $G/H$ are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection.
Bokan, Neda +2 more
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Axioms, 2022 The asymptotic behavior of resolvents of a proper convex lower semicontinuous function is studied in the various settings of spaces. In this paper, we consider the asymptotic behavior of the resolvents of a sequence of functions defined in a complete ...
Yasunori Kimura, Keisuke Shindo
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European Physical Journal C: Particles and Fields, 2022 For the gravitational wave model based on the type III Shapovalov wave space-time, test particle trajectories and the exact solution of geodesic deviation equations for the Bianchi type VII universe are obtained. Based on the found 4-vector of deviation,
Konstantin Osetrin +2 more
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Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations
Axioms, 2023 This paper investigates the existence and convergence of solutions for linear and nonlinear matrix equations. This study explores the potential of convex (α,β)-generalized contraction mappings in geodesic spaces, ensuring the existence of solutions for ...
Rahul Shukla, Winter Sinkala
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Geodesics in the space of Kähler metrics [PDF]
Duke Mathematical Journal, 2013 Let (X,ω) be a compact Kähler manifold. As discovered in the late 1980s by Mabuchi, the set H_0 of Kähler forms cohomologous to ωhas the natural structure of an infinite dimensional Riemannian manifold. We address the question whether any two points in H_0 can be connected by a smooth geodesic, and show that the answer, in general, is "no".
Lempert, László, Vivas, Liz
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