Results 1 to 10 of about 44,278 (213)
Contact Geometry of Curves [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group $G$. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit.
Peter J. Vassiliou
doaj +8 more sources
Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds [PDF]
, 2012 It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is ...
A. Banyaga +41 more
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Non-reductive spaces with equiaffine connections of nonzero curvature [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2021 The introduction of this article states the object of our investigation which is structures on homogeneous spaces. The problem of establishing links between the curvature and the structure of a manifold is one of the important problems of geometry.
Mozhey, Natal’ya Pavlovna
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Geometry-Preserving Numerical Methods for Physical Systems with Finite-Dimensional Lie Algebras [PDF]
Journal of nonlinear science, 2023 We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically associated with a Lie system on a general manifold via a Lie group action and ...
Luis Blanco Díaz +3 more
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Lie algebras of differentiations of linear algebras over a field
Дифференциальная геометрия многообразий фигур, 2021 In this paper, we study a system of linear equations that define the Lie algebra of differentiations DerA of an arbitrary finite-dimensional linear algebra over a field.
A. Ya. Sultanov +2 more
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Algebraic torus actions on contact manifolds [PDF]
Journal of differential geometry, 2018 We prove LeBrun-Salamon Conjecture in low dimensions. More precisely, we show that a contact Fano manifold X of dimension 2n+1 that has reductive automorphism group of rank at least n-2 is necessarily homogeneous.
Jaroslaw Buczy'nski +2 more
semanticscholar +1 more source
Geometry of Submanifolds and Homogeneous Spaces
, 2020 The present Special Issue of Symmetry is devoted into two important areas of global Riemannian geometry, namely submanifold theory and the geometry of Lie groups and homogeneous spaces.
G. Kaimakamis, A. Arvanitoyeorgos
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Spectral geometry, homogeneous spaces and differential forms with finite Fourier series [PDF]
, 2007 Let G be a compact Lie group acting transitively on Riemannian manifolds Mi and let π:M1 → M2 be a G-equivariant Riemannian submersion. We show that a smooth differential form ϕ on M2 has finite Fourier series on M2 if and only if the pull back π*ϕ has ...
C. Dunn, P. Gilkey, J. H. Park
semanticscholar +1 more source
Symplectic and Poisson Geometry on Loop Spaces of Manifolds and Nonlinear Equations [PDF]
, 1995 We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear equations of ...
Олег Иванович Мохов
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Yang-Mills Flow and Uniformization Theorems [PDF]
, 1997 We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds.
Chow B. +3 more
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