Search results for "Hermitian manifold"

TANGENTIAL DEFORMATIONS ON FIBRED POISSON MANIFOLDS

2005

In a recent article, Cattaneo, Felder and Tomassini explained how the notion of formality can be used to construct flat Fedosov connections on formal vector bundles on a Poisson manifold $M$ and thus a star product on $M$ through the original Fedosov method for symplectic manifolds. In this paper, we suppose that $M$ is a fibre bundle manifold equipped with a Poisson tensor tangential to the fibers. We show that in this case the construction of Cattaneo-Felder- Tomassini gives tangential (to the fibers) star products.

Volumes of certain small geodesic balls and almost-Hermitian geometry

1984

Let D be the characteristic connection of an almost-Hermitian manifold, V D m (r) the volume of a small geodesic ball for the connection D and C C D 1 the first non-trivial term of the Taylor expansion of V D m (r). NK-manifolds are characterized in terms of C C D 1 and a family of Hermitian manifolds for which ∫ M C C D 1 dvol is a spectral invariant is given and one proves that C C D 1 and the spectrum of the complex Laplacian, together, determine the class in which a compact Hermitian manifold lines.

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.

Hermitian natural differential operators

1986

Subharmonic variation of the leafwise Poincar� metric

2003

Let X be a compact complex algebraic surface and let F be a holomorphic foliation, possibly with singularities, on X. On each leaf of F we put its Poincare metric (this will be defined below in more precise terms). We thus obtain a (singular) hermitian metric on the tangent bundle TF of F , and dually a (singular) hermitian metric on the canonical bundle KF = T ∗ F of F . The main aim of this paper is to prove that this metric on KF has positive curvature, in the sense of currents. Of course, the positivity of the curvature in the leaf direction is an immediate consequence of the definitions; the nontrivial fact is that the curvature is positive also in the directions transverse to the leaf…