arXiv research

We develop a way of seeing a complete orientable hyperbolic $4$-manifold $\mathcal{M}$ as an orbifold cover of a Coxeter polytope $\mathcal{P} \subset \mathbb{H}^4$ that has a facet colouring. We also develop a way of finding totally geodesic sub-manifolds $\mathcal{N}$ in $\mathcal{M}$, and describing the result of mu…

The object of this paper is study $(ε)$-para-Sasakian 3-manifolds satisfying certain conditions on the $\mathcal{Z}$ tensor. We characterize, $\mathcal{Z}$-symmetric; $\mathcal{Z}$-semisymmetric; $\mathcal{Z}$-pseudosymmetric; and projectively $\mathcal{Z}$-semisymmetric conditions on an $(ε)$-para-Sasakian 3-manifold.

The paper classifies special types of contact metric manifolds with curvature conditions.

This paper studies algebraic fibrations in hyperbolic 4-manifolds.

This paper covers non-orientable Euclidean manifolds B3 and B4, detailing their n-fold coverings.

New findings on leafwise quasi-geodesic foliations in 3-manifolds.

New conditions for parabolicity and hyperbolicity of conductive Riemannian manifolds established.

This paper studies Hopf algebras from dg manifolds.

The space ${\mathcal A}$ of almost complex structures on a closed manifold $M$ is studied. A natural parametrization of the space ${\mathcal A}$ is defined. It is shown, that ${\mathcal A}$ is a infinite dimensional complex weak Pseudo-Riemannian manifold. A curvature of the space ${\mathcal A}$ is found. The space ${\…

New spectral sequence for $\mathcal{K}$-manifolds, computing cohomology and harmonic forms.

The paper generalizes structures for groups from curved spaces.

The purpose of this paper is to study $\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifolds of a paracosymplectic manifold $\widetilde{M}$. We prove that the distributions associated with the definition of $\mathcal{P}\mathcal{R}$-semi-invariant warped product submanifold $M$ are always integrable. A nece…

The paper explores anomalous subvarieties in hyperbolic 3-manifolds and their geometric implications.

We show that for any set of primes $\mathcal{P}$ there exists a space $M_{\mathcal{P}}$ which is a homology and cohomology 3-manifold with coefficients in $\mathbb{Z}_{p}$ for $p\in \mathcal{ P}$ and is not a homology or cohomology 3-manifold with coefficients in $\mathbb{Z}_q$ for $q\not\in \mathcal{ P}$. Moreover, $M…

The spaces of Riemannian metrics on a closed manifold $M$ are studied. On the space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak Riemannian structures are defined and the corresponding connections are studied. The space ${\mathcal AM}$ of associated metrics on a symplectic manifold $M,ω$ is consider…

Guilbault and author prove sufficient conditions for $\mathcal{Z}$-compactifiability of certain manifolds.

Researchers simplify the computation of diffeomorphism groups for Morse-Bott foliations.

The article derives integral formulas for foliated sub-Riemannian manifolds.

The paper proves a Liouville theorem for a specific type of harmonic maps on foliated manifolds.

This paper connects symplectic and Kähler manifolds via brane quantization.

We prove a definable version of the Whitney embedding theorem for abstract-definable $\mathcal{C}^p$ manifolds with $1\leq p<\infty$, namely: every abstract-definable $\mathcal{C}^p$ manifold is abstract-definable $C^p$ embedded into $R^N$, for some positive integer $N$. As a consequence, we show that every abstract-de…

An almost Clifford and an almost Cliffordian manifold is a $G$--structure based on the definition of Clifford algebras. An almost Clifford manifold based on $\mathcal O:= \cc l (s,t)$ is given by a reduction of the structure group $GL(km, \mathbb R)$ to $GL(m, {\mathcal O})$, where $k=2^{s+t}$ and $m \in \mathbb N$. An…

In this paper, we study a new generalized class of $\mathcal{P}\mathcal{R}$-warped product submanifolds under the name $\mathcal{P}\mathcal{R}$-pseudo-slant warped product submanifolds in para-Kähler manifolds $\bar{M}$. The results of existence and non-existence for $\mathcal{P}\mathcal{R}$-pseudo-slant warped product…

The article proves integral formulas for foliated sub-Riemannian manifolds.

The paper calculates the second variation of energy functions for families of canonically polarized manifolds.

Smooth approximations lead to homotopy equivalences in manifold spaces.

The Weyl tube theorem is extended to Kähler manifolds.

In this paper, we study $\mathcal{P}\mathcal{R}$-anti-slant warped product submanifold of a nearly paracosymplectic manifold $\widetilde{M}$. The necessary and sufficient condition is obtained for the distributions allied to the characterization of a $\mathcal{P}\mathcal{R}$-anti-slant submanifold being integrable and …

For any transversal-Courant algebroid $E$ on a foliated manifold $(M,\mathcal{F})$, and for any choice of a decomposition $TM=T\mathcal{F}\oplus Q$, we construct a Courant algebroid structure on $T\mathcal{F}\oplus T^*\mathcal{F}\oplus E$.

We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and $φ$-sectional curvature of indefinite almost $\…

Establishes a connection between skein modules and algebraic sets.

Efficiently simulates Langevin dynamics on manifold using diffusion maps and finite volume schemes.

Defines manifolds of mappings between function spaces and discusses their properties.

A new approach to Riemannian geometry using embedded and submersion structures.

The study proves a Liouville theorem for certain asymptotically conical Calabi-Yau manifolds.

We consider the problem of recovering a $d-$dimensional manifold $\mathcal{M} \subset \mathbb{R}^n$ when provided with noiseless samples from $\mathcal{M}$. There are many algorithms (e.g., Isomap) that are used in practice to fit manifolds and thus reduce the dimensionality of a given data set. Ideally, the estimate $…

Locally approximating groups of homeomorphisms reveal manifold properties.

We study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions, adjoints and self-adjointness of such realizations are discussed. We construct regu…

It is proved that the isometry classes of pointed connected complete Riemannian $n$-manifolds form a Polish space, $\mathcal{M}_*^\infty(n)$, with the topology described by the $C^\infty$ convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifo…

Minimal crystallizations bound for 3-manifolds with boundary.

Let $π: \mathcal{X}^* \rightarrow B^*$ be an algebraic family of compact Kähler manifolds of complex dimension $n$ with negative first Chern class over a punctured disc $B^*\in \mathbb{C}$. Let $g_t$ be the unique Kähler-Einstein metric on $\mathcal{X}_t= π^{-1}(t)$. We show that as $t\rightarrow 0$, $(\mathcal{X}_t, g…

Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincaré series associated with $\mathcal{T}$ and its counting functions, which encode rich topological information. Using the `per…

New theorem generalizes contact manifolds with symplectic properties.

Extends manifold theory to $\mathcal{I}$-graded manifolds.

Proves local bi-integrability of bi-Hamiltonian systems on real smooth manifolds.

We show that if $\mathcal{L}$ is a codimension-one lamination in a finite volume hyperbolic 3-manifold such that the principal curvatures of each leaf of $\mathcal{L}$ are all in the interval $(-δ,δ)$ for a fixed $δ\in[0,1)$ and no complimentary region of $\mathcal{L}$ is an interval bundle over a surface, then each bo…

Let $X$ be a compact manifold, $D$ a real elliptic operator on $X$, $G$ a Lie group, $P\to X$ a principal $G$-bundle, and ${\mathcal B}_P$ the infinite-dimensional moduli space of all connections $\nabla_P$ on $P$ modulo gauge, as a topological stack. For each $[\nabla_P]\in{\mathcal B}_P$, we can consider the twisted …

A manifold's co-invariant cohomology can be infinite-dimensional.