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The boundary value problem for Dirac-harmonic maps

Qun Chen, Jürgen Jost, Guofang Wang, Miaomiao Zhu (2013)

Journal of the European Mathematical Society

Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...

The BV-algebra of a Jacobi manifold

Izu Vaisman (2000)

Annales Polonici Mathematici

We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.

The Calabi functional on a ruled surface

Gábor Székelyhidi (2009)

Annales scientifiques de l'École Normale Supérieure

We study the Calabi functional on a ruled surface over a genus two curve. For polarizations which do not admit an extremal metric we describe the behavior of a minimizing sequence splitting the manifold into pieces. We also show that the Calabi flow starting from a metric with suitable symmetry gives such a minimizing sequence.

The canonical constructions of connections on total spaces of fibred manifolds

Włodzimierz M. Mikulski (2024)

Archivum Mathematicum

We classify classical linear connections A ( Γ , Λ , Θ ) on the total space Y of a fibred manifold Y → M induced in a natural way by the following three objects: a general connection Γ in Y → M , a classical linear connection Λ on M and a linear connection Θ in the vertical bundle V Y → Y . The main result says that if dim ( M ) ≥ 3 and dim ( Y ) - dim ( M ) ≥ 3 then the natural operators A under consideration form the 17 dimensional affine space.

The centre symmetry set

Peter Giblin, Paul Holtom (1999)

Banach Center Publications

A centrally symmetric plane curve has a point called it’s centre of symmetry. We define (following Janeczko) a set which measures the central symmetry of an arbitrary strictly convex plane curve, or surface in R 3 . We investigate some of it’s properties, and begin the study of non-convex cases.

Currently displaying 61 – 80 of 706