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Geodesic Vector Fields on a Riemannian Manifold [PDF]
Mathematics, 2020 A unit geodesic vector field on a Riemannian manifold is a vector field whose integral curves are geodesics, or in other worlds have zero acceleration. A geodesic vector field on a Riemannian manifold is a smooth vector field with acceleration of each of
Sharief Deshmukh +2 more
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A Note on Geodesic Vector Fields [PDF]
Mathematics, 2020 The concircularity property of vector fields implies the geodesicity property, while the converse of this statement is not true. The main objective of this note is to find conditions under which the concircularity and geodesicity properties of vector ...
Sharief Deshmukh +3 more
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A Note on Solitons with Generalized Geodesic Vector Field [PDF]
Symmetry, 2021 We consider a general notion of an almost Ricci soliton and establish some curvature properties for the case in which the potential vector field of the soliton is a generalized geodesic or a 2-Killing vector field. In this vein, we characterize trivial generalized Ricci solitons.
Adara M Blaga +2 more
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Geodesic and Newtonian Vector Fields and Symmetries of Mechanical Systems
Symmetry, 2023 Geodesic vector fields and other distinguished vector fields on a Riemann manifold were used in the study of free motions on such a manifold, and we applied the geometric Hamilton–Jacobi theory for the search of geodesic vector fields from Hamilton–Jacobi vector fields and the same for closed vector fields.
JOSÉ F Cariñena, Cariñena JOSÉ F
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Explicit Geodesic Projection Distance on the Statistical Manifold of Multivariate Elliptical Distributions [PDF]
EntropyGeodesic projection distances on statistical manifolds have been widely applied across various research fields. Nevertheless, the existing closed-form solution is only available for the Gaussian manifold.
Xiangbing Chen +2 more
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Mathematics, 2020 In the paper, we analyze the necessary efficiency conditions for scalar, vectorial and vector fractional variational problems using curvilinear integrals as objectives and we establish sufficient conditions of efficiency to the above variational problems.
Tiziana Ciano +3 more
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On the existence of geodesic vector fields on closed surfaces [PDF]
Theoretical and Applied MechanicsWe construct an example of a Riemannian metric on the 2-torus such that its universal cover does not admit global Riemann normal coordinates.
Matveev Vladimir S.
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Conical geodesic bicombings on subsets of normed vector spaces [PDF]
Advances in Geometry, 2019 Abstract We establish existence and uniqueness results for conical geodesic bicombings on subsets of normed vector spaces. Concerning existence, we give a first example of a convex geodesic bicombing that is not consistent. Furthermore, we show that under a mild geometric assumption on the norm a conical geodesic bicombing on an open ...
Giuliano Basso, Benjamin Miesch
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A vector momenta formulation of diffeomorphisms for improved geodesic regression and atlas construction [PDF]
2013 IEEE 10th International Symposium on Biomedical Imaging, 2013 This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used.
Nikhil Singh +2 more
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Geodesic vectors of (α, β)-metrics on hypercomplex 4-dimensional Lie groups [PDF]
Journal of HyperstructuresIn this paper, we consider invariant (α, β)-metrics and describe all geodesic vectors and investigate the set of all homogeneous geodesics on left invariant hypercomplex four dimensional simply connected Lie groups.
Milad Zeinali Laki, Dariush Latifi
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