arXiv research

Classification of hypersurfaces in homogeneous spaces with specific properties.

Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.

Eastwood and Ezhov generalized the Cayley surface to the Cayley hypersurface in each dimension, proved some characteristic properties of the Cayley hypersurface and conjectured that a homogeneous hypersurface in affine space satisfying these properties must be the Cayley hypersurface. We will prove this conjecture when…

Classifies homogeneous hypersurfaces in specific 4D geometries.

This paper classifies Möbius homogeneous hypersurfaces in a sphere.

The paper classifies homogeneous hypersurfaces in three 4D Thurston geometries.

Classifies curvature homogeneous hypersurfaces in S^4 and H^4.

We study the geometry of homogeneous hypersurfaces and their focal sets in complex hyperbolic spaces. In particular, we provide a characterization of the focal set in terms of its second fundamental form and determine the principal curvatures of the homogeneous hypersurfaces together with their multiplicities.

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

We classify the tube domains in C^4 with affinely homogeneous base whose boundary contains a non-degenerate affinely homogeneous hypersurface. It follows that these domains are holomorphically homogeneous and amongst them there are four new examples of unbounded homogeneous domains (that do not have bounded realisation…

The paper classifies hypersurfaces in a specific 4D geometry.

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.

Study classifies special Hessian rank 2 hypersurfaces in 4D space.

A Lie hypersurface in the complex hyperbolic space is a homogeneous real hypersurface without focal submanifolds. The set of all Lie hypersurfaces in the complex hyperbolic space is bijective to a closed interval, which gives a deformation of homogeneous hypersurfaces from the ruled minimal one to the horosphere. In th…

We classify all (locally) homogeneous Levi non-degenerate real hypersurfaces in $\mathbb{C}^3$ with symmetry algebra of dimension $\geq 6$.

We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.

Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of homogeneous Riemannian hypersurfaces and for the classification of linear transit…

The paper classifies various types of hypersurfaces in a product space.

Researchers calculate Morse index and nullity for two specific minimal hypersurfaces.

The paper classifies Hopf hypersurfaces with constant curvatures on complex quadrics.

In this paper, extending our previous joint work (Hu et al., Math Nachr 291:343--373, 2018), we initiate the study of Hopf hypersurfaces in the homogeneous NK (nearly Kähler) manifold $\mathbf{S}^3\times\mathbf{S}^3$. First, we show that any Hopf hypersurface of the homogeneous NK $\mathbf{S}^3\times\mathbf{S}^3$ does …

Hypersurfaces with constant Ricci eigenvalues in real space forms are classified.

The image of the Gauss map of any oriented isoparametric hypersurface of the unit standard sphere $S^{n+1}(1)$ is a minimal Lagrangian submanifold in the complex hyperquadric $Q_n({\mathbf C})$. In this paper we show that the Gauss image of a compact oriented isoparametric hypersurface with $g$ distinct constant princi…

Each hypersurface of a nearly Kähler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $φ$. In this paper, we show that, in the homogeneous NK $\mathbb{S}^6$ a hypersurface satisfies the condition $Aφ+φA=0$ if and only if it is …

Researchers classify hypersurfaces in specific symmetric spaces.

Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensiona…

To every Gorenstein algebra $A$ of finite dimension greater than 1 over a field ${\Bbb F}$ of characteristic zero, and a projection $π$ on its maximal ideal ${\mathfrak m}$ with range equal to the annihilator $\hbox{Ann}({\mathfrak m})$ of ${\mathfrak m}$, one can associate a certain algebraic hypersurface $S_π\subset{…

We exhibit a family of homogeneous hypersurfaces in affine space, one in each dimension, generalising the Cayley surface.

The study classifies isoparametric and homogeneous hypersurfaces in product spaces.

New classification of complex hypersurfaces using advanced algebraic methods.

The study classifies Hessian rank 1 hypersurfaces in dimensions 2, 3, and 4.

Hypersurfaces of manifolds of constant nonzero sectional curvature are classificated according their restricted homogeneous holonomy groups.

Study finds maximal symmetry groups for CR structures with specific properties.

Classifies special hypersurfaces in Gödel spacetimes.

Survey on extending rigidity theorems to Riemannian manifolds.

We introduce analogues of a map due to Rossi and show how they can be used to explicitly determine all covers of certain homogeneous strongly pseudoconvex 3-dimensional hypersurfaces that appear in the classification obtained by E. Cartan in 1932.

We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.

The study classifies isoparametric hypersurfaces in product spaces with constant angle function.

Study on stability of minimal submanifolds in specific Einstein manifolds.

In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of cohomogeneity one.

A Lie hypersurface in the complex hyperbolic space is an orbit of a cohomogeneity one action without singular orbit. In this paper, we classify Ricci soliton Lie hypersurfaces in the complex hyperbolic spaces.

We show that a simply connected Riemannian homogeneous space M which admits a totally geodesic hypersurface F is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped product of the Euclidean space and a homogeneous space, or (c) the twisted product o…

Classifies isoparametric hypersurfaces in 3D manifolds.

No non-product Hessian rank 1 affine homogeneous hypersurfaces exist in dimensions 5 and above.

Paper solves Dirichlet problem for $p$-convex hypersurfaces with curvature constraints.

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.

A method constructs invariant PDEs on homogeneous manifolds.

A new proof of the homogeneity of isoparametric hypersurfaces with six simple principal curvatures (Dorfmeister-Neher's theorem) is given in a method applicable to the multiplicity two case.