The Lp$L^p$‐diameter of the space of contractible loops
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area‐preserving diffeomorphisms endowed with the Lp$L^p$‐metric. As a special case, this resolves the Lp$L^p$‐metric analog of the well‐known question in symplectic topology ...
Michael Brandenbursky, Egor Shelukhin
wiley +1 more source
Lorentzian homogeneous structures with indecomposable holonomy
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract For a Lorentzian homogeneous space, we study how algebraic conditions on the isotropy group affect the geometry and curvature of the homogeneous space. More specifically, we prove that a Lorentzian locally homogeneous space is locally isometric to a plane wave if it admits an Ambrose–Singer connection with indecomposable, non‐irreducible ...
Steven Greenwood, Thomas Leistner
wiley +1 more source
Integrable Equations and Their Evolutions Based on Intrinsic Geometry of Riemann Spaces
International Journal of Mathematics and Mathematical Sciences, 2009 The intrinsic geometry of surfaces and Riemannian spaces will be investigated. It is shown that many nonlinear partial differential equations with physical applications and soliton solutions can be determined from the components of the relevant metric ...
Paul Bracken
doaj +1 more source
The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
, 2010 We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential map which allow us to describe the conjugate locus and the ...
Bonnard, Bernard +3 more
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Geometry of Foliated Manifolds
Extracta Mathematicae, 2016 In this paper some results of the authors on geometry of foliated manifolds are stated and results on geometry of Riemannian (metric) foliations are discussed.
A.Ya. Narmanov, A.S. Sharipov
doaj
Combinatorial Optimization with Information Geometry: The Newton Method
Entropy, 2014 e discuss the use of the Newton method in the computation of max(p → Εp [f]), where p belongs to a statistical exponential family on a finite state space.
Luigi Malagò, Giovanni Pistone
doaj +1 more source
Recognition of motor intentions from EEGs of the same upper limb by signal traceability and Riemannian geometry features. [PDF]
Front Neurosci, 2023 Zhang M, Huang J, Ni S.
europepmc +1 more source
Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices
Entropy, 2016 The Riemannian geometry of the space Pm, of m × m symmetric positive definite matrices, has provided effective ...
Hatem Hajri +4 more
doaj +1 more source
Corrigendum: Riemannian geometry-based metrics to measure and reinforce user performance changes during brain-computer interface user training. [PDF]
Front Comput Neurosci, 2023 Ivanov N, Chau T.
europepmc +1 more source
Riemannian Holonomy and Algebraic Geometry
, 1999 This survey paper is devoted to Riemannian manifolds with special holonomy. To any Riemannian manifold of dimension n is associated a closed subgroup of SO(n), the holonomy group; this is one of the most basic invariants of the metric.
Beauville, A.
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