Related papers: Non-orientable surfaces in 4-dimensional space
We study smooth proper embeddings of compact orientable surfaces in compact orientable $4$-manifolds and elements in the mapping class group of that surface which are induced by diffeomorphisms of the ambient $4$-manifolds. We call such…
In this paper, following Sullivan, Kusner, and Schmitt, we study conformal immersions of Riemann surfaces into the three-dimensional Euclidean space. Regarding such immersions as special bundle maps from the tangent bundle of the surface to…
We examine a model of non-self-avoiding, fluctuating surfaces as a candidate continuum string theory of surfaces in three dimensions. This model describes Dynamically Triangulated Random Surfaces embedded in three dimensions with an…
In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…
In this paper we will prove Hadamard-Stoker type theorems in the following ambient spaces: $\man ^n \times \r$, where $\man ^n $ is a $1/4-$pinched manifold, and certain Killing submersions, e.g., Berger spheres and Heisenberg spaces. That…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.
In this paper, we extend the investigation of biconservative surfaces with parallel normalized mean curvature vector fields (PNMC) in the 4-dimensional space forms, focusing on the hyperbolic space \mathbb{H}^4, the last remaining case to…
The paper is focused on the four-dimensional visualization of hypersurfaces represented by implicit equations without their parametrization. We describe a general method to find shadow boundaries in an arbitrary dimension and apply it in a…
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those…
Let M be an orientable and irreducible 3-manifold whose boundary is an incompressible torus. Suppose that M does not contain any closed nonperipheral embedded incompressible surfaces. We will show in this paper that the immersed surfaces in…
A \emph{surface of translation} is a sum $(u,v)\mapsto\gt\alpha(u)+\gt\beta(v)$ of two space curves: a \emph{path} $\gt\alpha$ and a \emph{profile} $\gt\beta$. A fundamental problem of differential geometry and shell theory is to determine…
The purpose of this paper is to present some results on the existence of homologous, nonisotopic symplectic or lagrangian surfaces embedded in a simply connected symplectic 4-dimensional manifold.
Minimal surfaces and Einstein manifolds are among the most natural structures in differential geometry. Whilst minimal surfaces are well understood, Einstein manifolds remain far less so. This exposition synthesises together a set of…
In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $L_1$. As a corollary, we obtain that all planar graphs which are 1-skeletons of planar non-positively…
We study the geodesics on an invariant surface of a three dimensional Riemannian manifold. The main results are: the characterization of geodesic orbits; a Clairaut's relation and its geometric interpretation in some remarkable three…
Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…
Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.
We present and apply a method for disproving the existence of polyhedral immersions in $\mathbb{R}^3$ of certain triangulations on non-orientable surfaces. In particular, it is proved that neither of the two vertex-minimal, neighborly…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…