Search results for "Complex manifold"
showing 6 items of 6 documents
Geodesics on spaces of almost hermitian structures
1994
A natural metric on the space of all almost hermitian structures on a given manifold is investigated.
Moment-angle complexes and complexe manifolds
2010
The aim of this thesis is to extend the results of the article [B-M] on the relations between moment-angle complexes and complex manifolds. We will focus here on moment-angle complexes defined by a simplicial (not only polytopal) decomposition of the sphere. We will also seek to use the relationship between these two kinds of objects to be understand the topology of several complex manifolds. [B-M] F.Bosio, L.Meersseman, Real quadrics in Cn, complex manifolds and polytopes, Acta Mathematica, 197 (2006), n° 1, 53 -- 127.
Observations on the Darboux coordinates for rigid special geometry
2006
We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\Lambda,q_\Lambda), I=1,...,2n$. The central role of the real $2n\times 2n$ matrix $M(\Re \mathcal{F},\Im \mathcal{F})$, where $\mathcal{F} = \partial_\Lambda\partial_\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\Omega M=\Omega$ with $\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\frac{\partial^2 S}{\partial P^I\partial P^J}$ of a certain hamiltonian real fun…
Real quadrics in C n , complex manifolds and convex polytopes
2006
In this paper, we investigate the topology of a class of non-Kähler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics Cn which are invariant with respect to the natural action of the real torus (S1)n onto Cn. The quotient space is a simple convex polytope. The problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes. We prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich. We also resolve an associated wall-cros…
The linearized Calderón problem on complex manifolds
2019
International audience; In this note we show that on any compact subdomain of a Kähler manifold that admits sufficiently many global holomorphic functions , the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of Kähler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot by treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holo-morphic functions with approximately prescribed critical points.…
On Hodge theory for the generalized geometry (I)
2013
Abstract We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kahler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context.