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该系列工作刻画和分类了切丛具有特定正性的全纯叶状结构和射影流形的整体几何结构。具体成果包括,第一陈类为nef的叶状结构研究,推广了Cao-Hoering的结构定理;切丛包含strictly nef子层的射影流形研究,延伸了Andreatta-Wisniewski定理;Fano流形切丛的big性判则。
Inspired by a recent result of Cho-Kim-Park, we consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound ...
Let ¯Li −→ Xi be a holomorphic line bundle over a compact complex manifold for i = 1, 2. Let Si denote the associated principal circle-bundle with respect to some hermitian inner product on...
This paper concerns the problem of integrability of non closed distributions on Banach manifolds. We introduce the notion of weak distribution and we look for conditions under which these distributi...
Let M be a CR submanifold of maximal CR dimension of a complex space form M. The shape operator A of the distinguished vector field is recurrent if there exists a 1-form v such that ∇A = A X...
The name “K3 surfaces” was coined by A. Weil in 1957 when he formulated a research programme for these surfaces and their moduli.
The study of the spectrum of the Laplace operator has been a very active subject in Riemannian geometry. In the compact case, the spectrum consists of eigenvalues.On a noncompact complete Riemannian m...
To study a noncompact Riemannian manifold, it is often useful to find a compactification or attach a boundary. For example, in hyperbolic geometry a lot of investigation is carried out on the sphere ...
We find new examples of compact Spin(7)-manifolds using a construction of Joyce [18, 19]. The essential ingredient in Joyce’s construction is a Calabi–Yau 4-orbifold with particular singularities admi...
It has been proved that there are no real hypersurfaces satisfying RA =0 in non-flat complex space forms. In this paper we prove that the same is true in the case of CR submanifolds of maximal CR dime...
Let us consider a Riemannian manifold M (either separable or non-separable). We prove that, for every " > 0, every Lipschitz function f : M ! R can be uniformly approximated by a Lipschitz, C1-smooth ...
We construct solutions of the constraint equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain expo...
We explore a new simple N = 2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holom...
Given (M, g0) we consider the problem −"2g0+hu + u = (u+)p−1 with (", h) ∈ (0, ¯") × B. Here B is a ball centered at 0 with radius  in the Banach space of all Ck symmetric covaria...
We prove a neighbourhood theorem for arbitrary knots in contact 3-manifolds. As an application we show that two topologically isotopic Legendrian knots in a contact 3-manifold become Legendrian isotop...

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