757 research outputs found
The geometry of a bi-Lagrangian manifold
This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds
endowed with two transversal Lagrangian foliations. We also study the
non-integrable case (i.e., a symplectic manifold endowed with two transversal
Lagrangian distributions). We show that many different geometric structures can
be attached to these manifolds and we carefully analyse the associated
connections. Moreover, we introduce the problem of the intersection of two
leaves, one of each foliation, through a point and show a lot of significative
examples.Comment: 30 page
Asymptotics for general connections at infinity
For a standard path of connections going to a generic point at infinity in
the moduli space of connections on a compact Riemann surface, we show
that the Laplace transform of the family of monodromy matrices has an analytic
continuation with locally finite branching. In particular the convex subset
representing the exponential growth rate of the monodromy is a polygon, whose
vertices are in a subset of points described explicitly in terms of the
spectral curve. Unfortunately we don't get any information about the size of
the singularities of the Laplace transform, which is why we can't get
asymptotic expansions for the monodromy.Comment: My talk at the Ramis conference, Toulouse, September 200
Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
We define and study projective special para-Kahler manifolds and show that
they appear as target manifolds when reducing five-dimensional vector
multiplets coupled to supergravity with respect to time. The dimensional
reductions with respect to time and space are carried out in a uniform way
using an epsilon-complex notation. We explain the relation of our formalism to
other formalisms of special geometry used in the literature. In the second part
of the paper we investigate instanton solutions and their dimensional lifting
to black holes. We show that the instanton action, which can be defined after
dualising axions into tensor fields, agrees with the ADM mass of the
corresponding black hole. The relation between actions via Wick rotation, Hodge
dualisation and analytic continuation of axions is discussed.Comment: 72 pages, 2 figure
- …