Related papers: Obstructions to embeddability into hyperquadrics a…

We develope in great computational details the classical Cartan equivalence problem for Levi-nondegenerate C^6-smooth real hypersurfaces M^3 in C^2, performing all calculations effectively in terms of a (local) graphing function \varphi. In…

We present results expressing conditions for the existence of meromorphic first integrals for Pfaff equations of arbitrary codimension, integrable or not, on complex manifolds. These results are in the same vein as previous ones by J-P.…

We study the contraction of strictly convex, axially symmetric hypersurfaces by a non-symmetric, non-homogeneous, fully nonlinear function of curvature. Starting from axially symmetric hypersurfaces with even profile curves, we show…

We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…

This article provides, over any field, infinitely many algebraic embeddings of the affine spaces $\mathbb{A}^1$ and $\mathbb{A}^2$ into smooth quadrics of dimension two and three respectively, which are pairwise non-equivalent under…

Let $M_\ell$ be a smooth Levi-nondegenerate hypersurface of signature $\ell$ in $\mathbf C^n$ with $ n\ge 3$, and write $H_\ell^N$ for the standard hyperquadric of the same signature in $\mathbf C^N$ with $N-n< \frac{n-1}{2}$. Let $F$ be a…

We use classical invariant theory to construct invariants of complex graded Gorenstein algebras of finite vector space dimension. As a consequence, we obtain a way of extracting certain numerical invariants of quasi-homogeneous isolated…

Given a unit vector field on a closed Euclidean hypersurface, we define a map from the hypersurface to a sphere in the Euclidean space. This application allows us to exhibit a list of topological invariants which combines the second…

The restriction problem is better understood for hypersurfaces and recent progresses have been made by bilinear and multilinear approaches and most recently polynomial partitioning method which is combined with those estimates. However, for…

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit…

When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers…

Non-existence theorems for Levi flat hypersurfaces have found great interest in the literature. The question next to this that has to be asked is, when existing Levi flat hypersurfaces are at least rigid under deformations. Here, the case…

We provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric…

Based on the results in [Rei14a] we deduce some topological results concerning holomorphic mappings of Levi-nondegenerate hyperquadrics under biholomorphic equivalence. We study the class $\mathcal F$ of so-called nondegenerate and…

We consider the question if a five dimensional manifold can be embedded into a Calabi-Yau manifold of complex dimension three such that the real part of the holomorphic volume form induces a given closed 3-form on the 5-manifold. We define…

In this note we motivate the definition and use of Lie algebroids by revisiting the problem of reconstructing a hypersurface in Euclidean space from infinitesimal data.

Using the $ku$- and $BP$-theoretic versions of Astey's cobordism obstruction for the existence of smooth Euclidean embeddings of stably almost complex manifolds, we prove that, for $e$ greater than or equal to $\alpha(n)$--the number of…

In this paper we collect some results on the obstruction spaces for rational surface singularities and minimally elliptic surface singularities. Based on the known results we calculate higher obstruction spaces for such surface…

We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi…

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…