相关论文: Extension of the unit normal vector field from a h…
We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
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…
We present an explicit formula for the mean curvature of a unit vector field on a Riemannian manifold, using a special but natural frame. As applications, we treat some known and new examples of minimal unit vector fields. We also give an…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…
Given a smooth curve $\gamma$ in some $m$-dimensional surface $M$ in $\mathbb{R}^{m+1}$, we study existence and uniqueness of a flat surface $H$ having the same field of normal vectors as $M$ along $\gamma$, which we call a flat…
In the case of simple graded manifolds utilized in supermechanics, supervector fields and exterior superforms are represented by global sections of smooth vector bundles.
Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately. Signed distance fields and occupancy fields are decades old and still the preferred representations, both with well-studied…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Hypergraphs are an invaluable tool to understand many hidden patterns in large data sets. Among many ways to represent hypergraph, one useful representation is that of weighted clique expansion. In this paper, we consider this…
The objective of the present paper (the second in a series of four) is to give a theory of multivector and extensor fields on a smooth manifold M of arbitrary topology based on the powerful geometric algebra of multivectors and extensors.…
In this paper we deal with relative normalizations of hypersurfaces in the (n+1)-dimensional Euclidean space $\mathbb{R}^{n+1}$. Considering a relative normalization $\bar{y}$ of an hypersurface $\Phi$ we decompose the corresponding…
The Castelnuovo-Mumford regularity r of a complex, projective variety V is an upper bound for the degrees of the hypersurfaces necessary to cut out V. In this note we give a bound for r when V is left invariant by a vector field on the…
It has recently been shown that the presence of a spectator pseudoscalar field, coupled to photons through a Chern-Simons term, can amplify the primordial tensor spectrum without observationally disrupting the primordial scalar spectrum.…
We use two ingredients to prove the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements in the complex projective space. One is the pullbacks of appropriate low pole order meromorphic jet…
We consider a unit normal vector field of (local) hyperfoliation on a given Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki metric. We give an explicit expression of the second fundamental form for this…
We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for…
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…
This note proposes a new notion of a gradient-like vector field and discusses its implications for the theory of Stein and Weinstein structures.
We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on…