arXiv research

New condition prevents hyperbolic spaces from matching curve complexes.

Classifies minimal submanifolds in complex hyperbolic spaces.

Classifies CR submanifolds in complex hyperbolic spaces.

Paper constructs Hopf real hypersurfaces in complex hyperbolic space.

We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted hypersurfaces of quaternionic hyperbolic space are also obtained.

Unique inhomogeneous ruled hypersurface found in complex hyperbolic space.

Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.

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.

New interpretation of complex hyperbolic form as Weil-Petersson form.

Compactifies CR structures for complex hyperbolic manifolds.

Study of holonomy algebras and Kahler homogeneous structures in complex hyperbolic spaces.

This paper classifies Ricci solitons in complex hyperbolic spaces.

We classify isoparametric hypersurfaces in complex hyperbolic spaces.

Study minimal surfaces in complex hyperbolic space, linking entropy and volume.

Study of quaternionic hyperbolic space bisectors and their decompositions.

Let $H^n$ denote the complex hyperbolic space of dimension $n$. The group $U(n,1)$ acts as the group of isometries of $H^n$. In this paper we investigate when two isometries of the complex hyperbolic space commute. Along the way we determine the centralizers.

We classify polar actions on complex hyperbolic spaces up to orbit equivalence.

We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.

Sharp inequalities on Siegel domains and complex hyperbolic spaces established.

Any Kaehler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dime…

Study properties of balanced hyperbolic compact complex manifolds.

The study determines discreteness of complex hyperbolic triangle groups.

First example of a hyperbolic 4-orbifold underlying $\mathbb{P}^2$.

We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.

New groups found with critical exponents close to but less than max.

These are lectures on discrete groups of isometries of complex hyperbolic spaces, aimed to discuss interactions between the function theory on complex hyperbolic manifolds and the theory of discrete groups.

The Complex of Curves on a Surface is a simplicial complex whose vertices are homotopy classes of simple closed curves, and whose simplices are sets of homotopy classes which can be realized disjointly. It is not hard to see that the complex is finite-dimensional, but locally infinite. It was introduced by Harvey as an…

We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian submersions from a complex pseudo-hyperbolic space onto a Riemannian manifold under the …

This paper proposes a spectral clustering algorithm for hyperbolic spaces, improving efficiency over Euclidean methods.

We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of minus and plus signs associated with the diagonalized metric matrix. The main resu…

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces of dimension greater than two. For the quaternionic hyperbolic spaces of dimension greater than two we reduce the classification problem to…

The space of marked n distinct points on the complex projective line up to projective transformations will be called a configuration space in this paper. There are two families of complex hyperbolic structures on the configuration space constructed by Deligne-Mostow and Thurston. We first confirm that these families ar…

This paper connects spinors to horospheres in hyperbolic space.

The study constructs minimal submanifolds in complex and quaternionic projective spaces.

Survey of group actions on hyperbolic spaces, focusing on mapping class groups and Out(F_n).

The paper defines two types of hyperbolicity for complex manifolds and proves related results.

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 study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with constant negative curvature. This study uses an interaction between Kähler geometr…

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove bot…

We classify pseudo-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a pseudo-Riemannian manifold. Also, we obtain the classification of the pseudo-Riemannian submersions with (para-)complex connected totally geodesic fibres from a (para-)complex pseudo-hyperbolic sp…

In this note, we study deformations of quaternionic hyperbolic lattices in larger quaternionic hyperbolic spaces and prove local rigidity results. On the other hand, surface groups are shown to be more flexible in quaternionic hyperbolic plane than in complex hyperbolic plane.

New Kähler manifolds found with nonpositive curvature operators.

We prove that, up to isometric congruence, there are exactly 2n+1 homogeneous polar foliations of the complex hyperbolic space. We also give an explicit description of each of these foliations.

A simplicial complex is called negatively curved if all its simplices are isometric to simplices in hyperbolic space, and it satisfies Gromov's Link Condition. We prove that, subject to certain conditions, a compact graph of spaces whose vertex spaces are negatively curved 2-complexes, and whose edge spaces are points …

We prove a positive mass theorem for complete Kähler manifolds that are asymptotic to the complex hyperbolic space.

Study complex hyperbolic lattices and their relation to strict hyperbolization.

Let $S$ be a closed, orientable surface of genus at least 2. The cotangent bundle of the "hyperbolic'' Teichmüller space of $S$ can be identified with the space $\CP$ of complex projective structures on $S$ through measured laminations, while the cotangent bundle of the "complex'' Teichmüller space can be identified wi…