Related papers: Submanifolds with ample normal bundle

We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold $\sigma$, we associate an integer-valued function, called degree, measuring the extent to which $\sigma$ fails to be cylindrical. In particular,…

Any closed orientable and smooth non-positively curved manifold M is known to admit a geometric characteristic splitting, analogous to the JSJ decomposition in three dimensions. We show that when this splitting consists of pieces which are…

Any line bundle $\cl $ on a smooth curve $C$ of genus $g$ with $\deg \cl \ge 2g+1$ is normally generated, i.e., $\varphi_\cl (C)\subseteq \mathbb P H^0 (C,\cl)$ is projectively normal. However, it has known that more various line bundles of…

We generalize the Donagi and Witten construction of a first obstruction class for splitting of a supermanifold via differential operators using the theory of $n$-fold vector bundles and graded manifolds. Applying the generalized…

We prove a conjecture of Menasco and Zhang that if a tangle is completely tubing compressible then it consists of at most two families of parallel strands. This is related to problems of graphs in 3-manifold. A 1-vertex graph $\Gamma$ in a…

Motivated by Gray's work on tube formulae for complex submanifolds of complex projective space equipped with the Fubini-Study metric, Riemannian foliations of projective space are studied. We prove that there are no complex Riemannian…

Let X be a smooth projective curve of genus g bigger then 2. For any vector bundle E on X let M_k(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0<k<r, x positive and either x less…

Let $X\subset P^n$ be a complex projective manifold of degree $d$ and arbitrary dimension. The main result of this paper gives a classification of such manifolds (assumed moreover to be connected, non-degenerate and linearly normal) in case…

For $n\geq 3$ and $r\geq n$, we show that there are rank-$r$ vector bundles on $\mathbb{P}^n$ with arbitrary homological dimension. We apply the Bernstein-Gel'fand-Gel'fand correspondence to translate the vector bundle question into a…

In this article, we construct the reduced genus-two Gromov-Witten invariants for certain almost K\"{a}hler manifold $(X, \omega, J)$ such that $J$ is integrable and satisfies some regularity conditions. In particular, the standard…

Nirenberg and Spencer posed the question whether the germ of a compact complex submanifold in a complex manifold is determined by its infinitesimal neighborhood of finite order when the normal bundle is sufficiently positive. To study the…

Suppose that $M$ is a $2$-dimensional oriented Riemannian manifold, and let $\gamma$ be a simple closed curve on $M$. Let $m \gamma$ denote the curve formed by tracing $\gamma$ $m$ times. We prove that if $m \gamma$ is contractible through…

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…

Germs of tubular neighborhood embeddings for submanifolds N of manifolds M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of `normal forms results' for geometric…

We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic…

We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.

Given a manifold with boundary, one can consider the space of subsurfaces of this manifold meeting the boundary in a prescribed fashion. It is known that these spaces of subsurfaces satisfy homological stability if the manifold has at least…

In this paper, we advance the classification of toric 2-Fano manifolds by continuing the investigation of the minimal projective bundle dimension $m(X) \in \{1,\dots,\dim(X)\}$ introduced in our previous work. This invariant captures the…

The purpose of this paper has twofold. The first is to prove a unicity theorem for meromorphic mappings of a complete K\"{a}hler manifold M in P^n(C) sharing few hypersurfaces. The second is to give a unicity theorem for the case of…

We address the following question: Given a differentiable manifold $M$ what are the open subsets $U$ of $M$ such that, for all vector bundles $E$ over $M$ and all linear connections $\nabla$ on $E$, any $\nabla$-parallel section in $E$…