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The aim of this paper is to extend the definition of geodesics to conical manifolds, defined as submanifolds of Rn with a finite number of singu-larities.
The covariant derivative of the K¨ahler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which s...
Let X be a complex manifold andM ⊂ X a compact, smooth, pseudoconvex CR manifold of dimension 2n − 1. (Here n ≥ 3 or, in case n = 2, it is made the extra assumption that ¯@b has close...
In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization ...
For a generic anti-canonical hypersurface in each smooth toric Fano 4−fold with rank 2 Picard group , we prove there exist three isolated rational curves in it . Moreover , for all these 4−...
Motivated by index theory on flag varieties, we prove a compactness theorem for products of longitudinal pseudodifferential operators on manifolds admitting multiple fibrations. Let X be a smooth mani...
We study the error in quadrature rules on a compact manifold, XN j=1 !jf (zj) − Z M f(x)dx ≤ cD {zj} V {f} .
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting.
A simple Hamiltonian manifold is a closed connected symplectic manifold equipped with a Hamiltonian action of a torus T with moment map  : M → t, such that MT has exactly two connected components, ...
We study symplectic structures on K¨ahler surfaces with pg = 0. We give an example of a projective surface which admits a symplectic structure which is not compatible with any K¨ahler metric.
We prove a general dispersive estimate for a Schr¨odinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates....
We will have a deep look at the set of all G-equivariant maps from the factor Lie group G to the under the action manifold M, both from “computationaland “observability” viewpoint. We will also be l...
We study the Berezin-Toeplitz quantization on K¨ahler manifolds. We explain first how to compute various associated asymptotic expansions, then we compute explicitly the first terms of the expansion o...
In this paper we study the homogeneous Kähler manifolds (h.K.m.) which can be Kähler immersed into finite or infinite dimensional complex space forms. On one hand we completely classify the ...
It is well known that the Hodge conjecture with rational coefficients holds for degree 2n − 2 classes on complex projective n-folds. In this paper we study the more precise question if on a rati...

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