Related papers: Embedding theorems for quasitoric manifolds
We prove that equivariant, holomorphic embeddings of Hermitian symmetric spaces are totally geodesic (when the image is not of exceptional type).
Quasitoric manifolds are manifolds that admit an action of the torus that is locally as the standard action of T^n on C^n. It is known that the quotients of such actions are nice manifolds with corners. We prove that such manifolds are…
We study open equivariant projective embeddings of homogeneous spaces such that the complement of the open orbit does not contain divisors. Criterions of existence of such an embedding are considered and finiteness of isomorphism classes of…
In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.
In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes,…
Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood…
We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.
We compute the homotopy type of the space of T^n-equivariant symplectic embeddings from the standard 2n-dimensional ball of some fixed radius into a 2n-dimensional symplectic-toric manifold M, and use this computation to define a Z-valued…
Totally skew embeddings are introduced by Ghomi and Tabachnikov. They are naturally related to classical problems in topology, such as the generalized vector field problem and the immersion problem for real projective spaces. In recent…
Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…
We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold is Hamiltonian. In this case, we may…
The polynomial invariants $q_d$ for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples.…
Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
In this paper we develop a theory of volume polynomials of generalized virtual polytopes based on the study of topology of affine subspace arrangements in a real Euclidean space. We apply this theory to obtain a topological version of the…
In this work we prove the fact that, for a short time, it is possible to construct a smooth parametrized family of isometric embeddings of an arbitrary smooth parametrized family of Riemannian metrics on a smooth closed manifold into an…
We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds…