Results 31 to 40 of about 892 (193)
Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds
Entropy, 2016 We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and
Stefan Sommer
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Journal of Differential Geometry, 1986 A sub-Riemannian or singular Riemannian geometry is given by a smoothly varying positive definite quadratic form defined only on a subbundle \(S\) of the tangent bundle \(TM\) of a differentiable manifold, \(S\) being bracket-generating, that is sections of \(S\) together with their Lie brackets generate the \(C^{\infty}(M)\)-module \(V(M)\) of vector ...
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Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, copepod nauplii and copepod robot
Pacific Journal of Mathematics for Industry, 2018 The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the
Bernard Bonnard +3 more
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On 4-dimensional Einsteinian manifolds with parallel null distribution [PDF]
ریاضی و جامعه, 2023 In this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this purpose, we first obtain the equations, which are known as Einstein's equations, that lead to finding the mentioned manifolds and then, we reduce Einstein's
Mehdi Jafari
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Corrections to: ``Sub-Riemannian geometry'' [PDF]
Journal of Differential Geometry, 1989 An error in the proof of Corollary 6.2 of [1] has been pointed out by Gerard Ben-Arous. The computation of M(x,λ) in the case λo = 0 on p. 243 is incorrect, because M(x,λ) = 0 when λ0 = 0 and λjg (x) = 0 for all k. (There is also a factor of \ missing in the formula as stated for λ0 φ 0, but this is not significant.) Thus when applying the Pontryagin ...
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On geometry of sub-Riemannian η-Einstein manifolds
Дифференциальная геометрия многообразий фигур, 2019 On a sub-Riemannian manifold of contact type a connection with torsion is considered, called in the work a Ψ-connection. A Ψ-connection is a particular case of an N-connection.
S. Galaev
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Nonholonomic Systems and Sub-Riemannian Geometry [PDF]
Communications in Information and Systems, 2010 This paper presents several classical mechanical systems with nonholonomic con- straints from the point of view of sub-Riemannian geometry. For those systems that satisfy the bracket generating condition the system can move continuously between any two given states.
Calin, Ovidiu +2 more
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The regularity problem for geodesics of the control distance
Bruno Pini Mathematical Analysis Seminar, 2018 In this survey, we present some recent results on the problem about the regularity of length-minimizing curves in sub-Riemannian geometry. We also sketch the possible application of some ideas coming from Geometric Measure Theory.
Roberto Monti
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Gauss-Bonnet theorem in Lorentzian Sasakian space forms
AIMS Mathematics, 2021 In this paper, we use a Lorentzian approximation scheme to compute the sub-Lorentzian limit of curvatures for curves and Lorentzian surfaces in the Lorentzian Bianci-Cartan-Vranceanu model of 3-dimensional Lorentzian Sasakian space forms.
Haiming Liu, Jiajing Miao
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The left-invariant contact metric structure on the Sol manifold
Учёные записки Казанского университета: Серия Физико-математические науки, 2020 Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple ...
V.I. Pan’zhenskii, A.O. Rastrepina
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