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Displaying 221 – 240 of 707

The geometry of the space of Cauchy data of nonlinear PDEs

Giovanni Moreno (2013)

Open Mathematics

First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given in many equivalent ways - for instance, by means of Grassmann bundles. In this paper we generalize it by means of flag bundles, and develop the corresponding theory for higher-oder and infinite-order jet bundles. We show that this is a natural geometric framework...

The global structure of constant mean curvature surfaces.

Nick Korevaar, Rob Kusner (1993)

Inventiones mathematicae

The global theory of doubly periodic minimal surfaces.

W.H. III Meeks, H. Rosenberg (1989)

Inventiones mathematicae

The Gluck and Ziller problem with the euclidean metric

Vincent Borrelli (2003/2004)

Séminaire de théorie spectrale et géométrie

The graded differential geometry of mixed symmetry tensors

Andrew James Bruce, Eduardo Ibarguengoytia (2019)

Archivum Mathematicum

We show how the theory of $ℤ_{2}^{n}$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

The graded representations of an affine Lie algebra

Futorny, V. M. (1991)

Proceedings of the Winter School "Geometry and Physics"

The $ℤ$ -graded symplectic Floer cohomology of monotone Lagrangian submanifolds.

Li, Weiping (2004)

Algebraic & Geometric Topology

The gradient flow of Higgs pairs

Jiayu Li, Xi Zhang (2011)

Journal of the European Mathematical Society

We consider the gradient flow of the Yang–Mills–Higgs functional of Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a Kähler surface $(M, ω)$ , and study the asymptotic behavior of the heat flow for Higgs pairs at infinity. The main result is that the gradient flow with initial condition $(A_{0}, φ_{0})$ converges, in an appropriate sense which takes into account bubbling phenomena, to a critical point $(A_{\infty}, φ_{\infty})$ of this functional. We also prove that the limiting Higgs pair $(A_{\infty}, φ_{\infty})$ can be extended smoothly to a vector bundle $E_{\infty}$ over...

The graph of a totally geodesic foliation

Robert A. Wolak (1995)

Annales Polonici Mathematici

We study the properties of the graph of a totally geodesic foliation. We limit our considerations to basic properties of the graph, and from them we derive several interesting corollaries on the structure of leaves.

The Gromov invariant and the Donaldson-Smith standard surface count.

Usher, Michael (2004)

Geometry & Topology

The Gromov Norm of the Kaehler Class of Symmetric Domains.

Domingo Toledo, Antun Domic (1986)

Mathematische Annalen

The Gromov width of complex Grassmannians.

Karshon, Yael, Tolman, Susan (2005)

Algebraic & Geometric Topology

The group of biholomorphic automorphisms of symmetric Siegel domains and its topology

José-María Isidro, Jean-Pierre Vigué (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Group of Invertible Elements of the Algebra of Quaternions

Irina A. Kuzmina, Marie Chodorová (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We have, that all two-dimensional subspaces of the algebra of quaternions, containing a unit, are 2-dimensional subalgebras isomorphic to the algebra $ℂ$ of complex numbers. It was proved in the papers of N. E. Belova. In the present article we consider a 2-dimensional subalgebra $(i)$ of complex numbers with basis $1, i$ and we construct the principal locally trivial bundle which is isomorphic to the Hopf fibration.

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