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Special invariant operators I

Jarolím Bureš (1996)

Commentationes Mathematicae Universitatis Carolinae

The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type G / B which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup B of the Lie group G . One example of an operator of this type is the Penrose’s local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more...

Structure of second-order symmetric Lorentzian manifolds

Oihane F. Blanco, Miguel Sánchez, José M. Senovilla (2013)

Journal of the European Mathematical Society

𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠 , that is to say, Lorentzian manifolds with vanishing second derivative ∇ ∇ R ≡ 0 of the curvature tensor R , are characterized by several geometric properties, and explicitly presented. Locally, they are a product M = M 1 × M 2 where each factor is uniquely determined as follows: M 2 is a Riemannian symmetric space and M 1 is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., ∇ R ≠ 0 at some point), the curvature tensor turns out to...

Symmetries of connections on fibered manifolds

Alexandr Vondra (1994)

Archivum Mathematicum

The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.

Symmetry of local minimizers for the three-dimensional Ginzburg–Landau functional

Vincent Millot, Adriano Pisante (2010)

Journal of the European Mathematical Society

We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in H loc 1 ( ℝ 3 ; ℝ 3 ) satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.

The gap phenomenon in the dimension study of finite type systems

Boris Kruglikov (2012)

Open Mathematics

Several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case when the structure is associated to a vector distribution, is proposed.

Currently displaying 61 – 80 of 96