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Arnold conjectured that every Legendrian knot in the standard contact structure on the 3-sphere possesses a haracteristic chord with respect to any contact form. I confirm this conjecture if the know has Thurston-Bennequin invariant $- 1$ . More generally, existence of chords is proved for a standard Legendrian unknot on the boundary of a subcritical Stein manifold of any dimension. There is also a multiplicity result which implies in some situations existence of infinitely many chords. The proof relies...

H-anti-invariant submersions from almost quaternionic Hermitian manifolds

Kwang-Soon Park (2017)

Czechoslovak Mathematical Journal

As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples...

Hard balls gas and Alexandrov spaces of curvature bounded above.

Burago, Dmitri (1998)

Documenta Mathematica

Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry

Laurent Bruasse, Andrei Teleman (2005)

Annales de l’institut Fourier

We give here a generalization of the theory of optimal destabilizing 1-parameter subgroups to non algebraic complex geometry : we consider holomorphic actions of a complex reductive Lie group on a finite dimensional (possibly non compact) Kähler manifold. In a second part we show how these results may extend in the gauge theoretical framework and we discuss the relation between the Harder-Narasimhan filtration and the optimal detstabilizing vectors of a non semistable object....

Hardy inequalities in strips on ruled surfaces.

Krejčiřík, David (2006)

Journal of Inequalities and Applications [electronic only]

Hardy spaces on affine symmetric spaces.

J. Hilgert, G. Olafsson, B. Orsted (1991)

Journal für die reine und angewandte Mathematik

Harmonic 4-Spaces.

S.M. Salamon (1984)

Mathematische Annalen

Harmonic almost-complex structures

C. M. Wood (1995)

Compositio Mathematica

Harmonic analysis and Radon transforms on pencils of geodesics.

E. Badertscher (1986)

Mathematica Scandinavica

Harmonic Analysis for Vector Fields on Hyperbolic Spaces.

H.M. Reimann, E. Badertscher (1989)

Mathematische Zeitschrift

Harmonic and Minimal Unit Vector Fields on the Symmetric Spaces $G_{2}$ and $G_{2} / S O (4)$

László Verhóczki (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The exceptional compact symmetric spaces $G_{2}$ and $G_{2} / S O (4)$ admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.

Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows

Fang Hua Lin, Chang You Wang (2002)

Annales de l'I.H.P. Analyse non linéaire

Harmonic cohomology classes of symplectic manifolds.

Olivier Mathieu (1995)

Commentarii mathematici Helvetici

Harmonic conformal flows on manifolds of constant curvature

Amine Fawaz (2007)

Open Mathematics

We compute the energy of conformal flows on Riemannian manifolds and we prove that conformal flows on manifolds of constant curvature are critical if and only if they are isometric.

Harmonic curvatures in Lorentzian space.

Ekmekçi, Nejat, Hacisalihoǧlu, H.Hilmi, İlarslan, Kāzim (2000)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Harmonic diffeomorphisms and Teichmüller theory.

Jochen Lohkamp (1991)

Manuscripta mathematica

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