arXiv research

Geometrically proves Lie algebras are identified by their Iwasawa subalgebras.

Study of double complexes on Iwasawa manifold yields 3 isomorphism types.

This paper classifies Ricci soliton subgroups in a specific type of nilpotent group.

Constructs explicit p-harmonic functions on specific Lie groups.

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_ε-$Iwasawa decomp…

Classifies Ricci soliton subgroups in specific Lie groups.

Analogues of Iwasawa invariants in the context of 3-dimensional topology have been studied by M.~Morishita and others. In this paper, following the dictionary of arithmetic topology, we formulate an analogue of Kida's formula on $λ$-invariants in a $p$-extension of $\mathbb{Z}_p$-fields for 3-manifolds. The proof is gi…

New Einstein metrics found on specific Lie algebras.

Study $p$-torsion growth in covers of 3-manifolds, proving Iwasawa formulas.

New method constructs translationally equivariant hyperbolic affine spheres.

Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient of the group of complex unipotent $3 \times 3$ matrices by a cocompact lattice. We prove that any compact complex curve in an Iwasawa manifold is contained in a holomorphic torus. We also prove that any Kähler surface in an Iwasawa mani…

Based on the analogy between knots and primes, J. Hillman, D. Matei and M. Morishita defined the Iwasawa invariants for sequences of cyclic covers of links with an analogue of Iwasawa's class number formula of number fields. In this paper, we consider the existence of covers of links with prescribed Iwasawa invariants,…

Study models of Gödel Universe using Lie groups and Iwasawa decomposition.

We identify the space of left-invariant oriented complex structures on the complex Heisenberg group, and prove that it has the homotopy type of the disjoint union of a point and a 2-sphere.

Study of knot invariants using twisted Iwasawa theory.

We set up an abstract framework that allows the investigation of Iwasawa decompositions for involutive infinite-dimensional Lie groups modeled on Banach spaces. As an application, we construct Iwasawa decompositions for classical real or complex Banach-Lie groups associated with the Schatten ideals ${\mathfrak S}_p({\m…

Study topological Iwasawa invariants for 3-sphere links, proving density results.

The paper constructs pseudo-Iwasawa solvmanifolds with Killing spinors.

We determine the successive pages of the Frölicher spectral sequence of the Iwasawa manifold and some of its small deformations, providing new examples and counterexamples on its properties, including the behaviour under small deformations.

The paper classifies and describes translators in $SL(2,\mathbb{R})$ under specific symmetry conditions.

Classifies CR submanifolds in complex hyperbolic spaces.

We prove that, for some classes of complex nilmanifolds, the Bott-Chern cohomology is completely determined by the Lie algebra associated to the nilmanifold with the induced complex structure. We use these tools to compute the Bott-Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, com…

We prove that the three-dimensional Iwasawa manifold $X$, viewed as a locally holomorphically trivial fibration by elliptic curves over its two-dimensional Albanese torus, is self-dual in the sense that the base torus identifies canonically with its dual torus under a sesquilinear duality, the Jacobian torus of $X$, wh…

Develops a new representation for constant mean curvature surfaces in hyperbolic 3-space.

For a unitary local system of rank one on a complete hyperbolic threefold of finite volume which has only one cusp, we will compare the order of the Alexander invariant at t=1 and one of Ruelle-Selberg L-function at s=0. Our result may be considered as a geometric analog of the Iwasawa main conjecture in the algebraic …

For a local system on a compact hyperbolic threefold, under a cohomological assumption, we will show that the order of its twisted Alexander polynomial and of the Ruelle L function at $s=0$ coincide. Moreover we will show that their leading constant are also identical. These results may be considered as a solution of a…

Formula derived for Bott-Chern classes in complex blow-ups.

Global harmonic maps into SU(1,1) constructed from Smyth potentials using DPW method.

This paper classifies Ricci solitons in complex hyperbolic spaces.

Introduces new holomorphic contact structures and proves unobstructedness theorems.

We propose a new approach to the Mirror Symmetry Conjecture in a form suitable to possibly non-Kähler compact complex manifolds whose canonical bundle is trivial. We apply our methods by proving that the Iwasawa manifold $X$, a well-known non-Kähler compact complex manifold of dimension $3$, is its own mirror dual to t…

This thesis was inspired by work of M. Cowling, F. De Mari, A. Koranyi and M. Reimann, who studied multicontact structures for the homogeneous manifolds G/P, where G is a semisimple Lie group and P is the minimal parabolic subgroup of G. The multicontact structure here arises naturally by the nilpotent component N of t…

We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action - by the whole subgroup of loops which extend holomorphically to the exterior disc - on the $U$-hierarchy of the ZS-AKN…

We show that all 6-dimensional nilmanifolds admit generalized complex structures. This includes the five classes of nilmanifold which admit no known complex or symplectic structure. Furthermore, we classify all 6-dimensional nilmanifolds according to which of the four types of left-invariant generalized complex structu…

We discuss the mathematical properties of six--dimensional non--Kähler manifolds which occur in the context of ${\cal N}=1$ supersymmetric heterotic and type IIA string compactifications with non--vanishing background H--field. The intrinsic torsion of the associated SU(3) structures falls into five different classes. …

Study of Alexander polynomials of torus knots and links, showing zeros equidistribute on unit circle.

In the first part we define a "BTZ" black hole in anti de Sitter space in any dimension by defining as "singular" the closed orbits of the Iwasawa component of SO(2,n). In the second part, a strict quantization of the black hole by action of group is performed and its Dirac operator is computed. We introduce, in the ap…

In this article we continue the study of the geometry of $k$-D'Atri spaces, $$ $\leq n-1$ ($n$ denotes the dimension of the manifold)$,$ began by the second author. It is known that $k$-D'Atri spaces, $k\geq 1,$ are related to properties of Jacobi operators $R_{v}$ along geodesics, since she has shown that ${\…

Study of deformed Bott-Chern cohomology on complex manifolds.

We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SU(1,n). This answers a question raised by Rieffel.

Extends deformation theory to higher-page analogues of manifolds.

We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. We also derive ex…

Study on existence of balanced metrics on non-Kähler manifolds.

This article introduces the problem of finding intrinsic torsion varieties associated to G-structures on a fixed parallelizable Riemannian manifold. As an illustration, the intrinsic torsion varieties of orthogonal almost product structures are analysed on the Iwasawa manifold.

Study on special metrics and deformations of solvmanifolds.

We study the relevant structure of so(2,n) which makes the BTZ black hole possible in the anti de Sitter space. We pay a particular attention of the reductive Lie algebra structures and Iwasawa decompositions and the way these structures evolves when one increases the dimension. The singularity is defined as the closed…

We factorize harmonic maps with values in a semisimple Lie groups in a product of harmonic maps with values in the components of the Iwasawa decomposition. In particular, we use this factorization to study the harmonic maps from $\mathbb{R}^n$ into $SL(2,\mathbb{R})$.

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.