arXiv research

The paper classifies special geometric shapes in 2D and 3D.

Ancient solutions to Kähler Ricci flow classified completely.

Complete classification of symmetric spaces actions.

Study of 3D vacuum static spaces with specific curvature properties.

We complete a minor gap in Gromoll and Walschap classification of metric fibrations from the Euclidean space, thus completing the classification of Riemannian foliations on Euclidean spaces.

Completed classification of Einstein spaces with specific metric properties.

The paper classifies 2D complete Lagrangian self-expanders in complex 2-space.

Complete classification of knotoids up to seven crossings.

We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.

In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable.

In this paper, we study biconservative hypersurfaces in the four dimensional Minkowski space $\mathbb E^4_1$. We give the complete explicit classification of biconservative hypersurfaces with diagonalizable shape operator in $\mathbb E^4_1$.

The study classifies certain types of incomplete surfaces with low curvature.

Classifies surfaces with no Gaussian curvature.

The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss-Kronecker curvature and scalar curvature bounded from below.

Complete classification of quaternionic skew-Hermitian symmetric spaces found.

This paper classifies solutions for a specific geometric problem.

In this paper we complete the classification of topological symmetry groups for complete graphs $K_n$ by characterizing which $K_n$ can have a cyclic group, a dihedral group, or a subgroup of $D_m \times D_m$ where $m$ is odd, as its topological symmetry group.

Complete classification of homogeneous real hypersurfaces in complex 3-space.

In this paper we give a complete local parametric classification of the hypersurfaces with dimension at least three of a space form that carry a totally geodesic foliation of codimension one. A classification under the assumption that the leaves of the foliation are complete was given in \cite{drt} for Euclidean hypers…

The paper classifies 3D complete gradient Yamabe solitons.

In this paper, we study locally strongly convex centroaffine hypersurfaces with parallel cubic form with respect to the Levi-Civita connection of the centroaffine metric. As the main result, we obtain a complete classification of such centroaffine hypersurfaces. The result of this paper is a centroaffine version of the…

The purpose of this paper is to study complete $λ$-surfaces in Euclidean space $\mathbb R^3$. A complete classification for 2-dimensional complete $λ$-surfaces in Euclidean space $\mathbb R^3$ with constant squared norm of the second fundamental form is given.

We give a complete topological classification of minimal surfaces in Euclidian three-space.

This paper completes the classification of discrete conformal structures on surfaces.

Complete classification of para-Kähler structures on Lie groups.

Study LCP structures on solvmanifolds, complete list up to 5 dimensions.

Proves classification of 4D complete intersections up to diffeomorphism.

Classification of cubics (that is, third order planar curves in the $R^2$ up to certain transformations is interested since Newton, and treated by several authors. We classify cubics up to affine transformations, in seven class, and give a complete set of representatives of the these classes. This result is complete an…

This paper completes the classification of certain nilpotent Lie groups with specific geometric structures.

The purpose of this paper is to study complete self-shrinkers of mean curvature flow in Euclidean spaces. In the paper, we give a complete classification for 2-dimensional complete Lagrangian self-shrinkers in Euclidean space $\mathbb R^4$ with constant squared norm of the second fundamental form.

Complete classification of links up to specific moves.

We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the 3-sphere. As an appendix, we also show that the Montesinos knots M (-1/2, 2/5, 1/(2q + 1)) with q at least 5 have no non-trivial exceptional surgeries. This gives the final step in a complete classification of exceptional …

We give an alternative proof to Agol's classification of parabolic generating pairs of non-free Kleinian groups generated by two parabolic transformations. As an application, we give a complete characterisation of epimorphims between $2$-bridge knot groups and a complete characterisation of degree one maps between the …

Paper classifies pseudomanifolds over stratified spaces.

This paper classifies complete self-shrinkers in R^(n+1) with nonnegative constant scalar curvature.

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

We determine all complete projective special real surfaces. By the supergravity r-map, they give rise to complete projective special Kähler manifolds of dimension 6, which are distinguished by the image of their scalar curvature function. By the supergravity c-map, the latter manifolds define in turn complete quaternio…

Complete classification of handlebody links up to six crossings.

Complete shrinking soliton found on a specific complex surface.

We give a complete classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient manifold. The results are analogues of Haefliger's classification of foliations on open manifold.

A complete classification of left-invariant closed G2-structures on Lie groups which are extremally Ricci pinched, up to equivalence and scaling, is obtained. There are five of them, they are defined on five different completely solvable Lie groups and the G2-structure is exact in all cases except one, given by the onl…

The main purpose of this paper is to complete the work initiated by Sbrana in 1909 giving a complete local classification of the nonflat infinitesimally bendable hypersurfaces in Euclidean space.

One of the current issues in Brain-Computer Interface is how to deal with noisy Electroencephalography measurements organized as multidimensional datasets. On the other hand, recently, significant advances have been made in multidimensional signal completion algorithms that exploit tensor decomposition models to captur…

In this paper, we classify 3-dimensional complete gradient Yamabe solitons with divergence-free Cotton tensor. We also give some classifications of complete gradient Yamabe solitons with nonpositively curved Ricci curvature in the direction of the gradient of the potential function.

Study geodesic curves on Heisenberg group, classify them, and compute first step of quadrature.

The authors give a complete classification of projective threefolds admitting a holomorphic conformal structure. A Corollary is the complete list of projective threefolds, whose tangent bundle is a symmetric square.

Completes classification of G2-structures on specific nilpotent Lie groups.

We study symmetric affine surfaces which have non-vanishing torsion tensor. We give a complete classification of the local geometries possible if the torsion is assumed parallel. This generalizes a previous result of Opozda in the torsion free setting; these geometries are all locally homogeneous. If the torsion is not…