arXiv research

We study the $(2+2)$-Einstein warped product manifolds, where the scalar curvature of the Base is a multiple of the warping function, and we called this condition (inside a warped product manifold) $f$-curvature-Base ($R_{f_B}$).The aim of this paper is to check if there are Base-manifolds with non-flat metrics that sa…

A new metric-based principal curve method learns 1D manifolds from spatial data.

For the studied cases in [10], the author showed that having the {\textit {$f$-curvature-Base}} ($R_{f_B}$) is equal to requiring a flat metric on the base-manifold. In [11] the authors introduced a new kind of Einstein warped product manifold, composed by positive-dimensional manifold and negative-dimensional manifold…

Study Einstein warped products with Einstein base and fiber.

The paper studies Riemannian maps with Ricci soliton base manifolds.

The based loop space homology of a special family of homogeneous spaces, flag manifolds of connected compact Lie groups is studied. First, the rational homology of the based loop space on a complete flag manifold is calculated together with its Pontrjagin structure. Second, it is shown that the integral homology of the…

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…

Study pin manifolds using Clifford linear Dirac operator and KO-theory.

Extends geometrical description of tensor manifolds in tree-based formats.

RSGMs extend SGMs to Riemannian manifolds for better data modeling.

Develop intrinsic consensus-based optimization framework on Riemannian manifolds with bounded curvature.

In this paper we give a method to construct Heegaard splittings of oriented graph manifolds with orientable bases. A graph manifold is a closed $3$-manifold admitting only Seifert-fibered pieces in its Jaco-Shalen decomposition; for technical reasons, we restrict our attention to the fully oriented case, i.e. both the …

We derive a formula for the Dijkgraaf-Witten invariants of orientable Seifert 3-manifolds with orientable bases.

The paper studies Clairaut maps on Sasakian manifolds.

We compute the curvature tensor of the tangent bundle of a Riemannian manifold endowed with a natural metric and we get some relationships between the geometry of the base manifold and the geometry of the tangent bundle.

Simplifies denoising score matching for manifold learning.

Isomorphic cosymplectomorphism groups imply diffeomorphic manifolds.

We construct new examples of manifolds with cyclic-parallel Ricci tensor, so called A-manifolds, on a r-torus bundle over a product of almost Hodge A-manifolds.

The paper studies maps between Riemannian and Kähler manifolds, focusing on Clairaut semi-invariant Riemannian maps.

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the $η$-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is $η$-E…

Study graph-based algorithms for multi-manifold clustering with sufficient conditions.

Paper proposes methods to learn sub-manifolds and estimate densities in normalizing flows.

The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.

Existence of hypersurfaces in warped product manifolds proven.

We use Heath's, Moriah's and Schultens's results to prove that irreducible Heegaard splittings of orientable Seifert manifolds with nonorientable base space are either vertical or horizontal.

The tangent bundle of an almost Norden manifold and the complete lift of the Norden metric is considered as a 4n-manifold. It is equipped with an almost hypercomplex Hermitian-Norden structure. It is characterized geometrically. The case when the base manifold is an h-sphere is considered.

Deep neural networks (DNNs) have been successfully applied to a wide variety of acoustic modeling tasks in recent years. These include the applications of DNNs either in a discriminative feature extraction or in a hybrid acoustic modeling scenario. Despite the rapid progress in this area, a number of challenges remain …

It is proven that a local Lie algebra in the sense of A. A. Kirillov determines the base manifold up to a diffeomorphism provided the anchor map is nowhere-vanishing. In particular, the Lie algebras of nowhere-vanishing Poisson or Jacobi brackets determine manifolds. This result has been proven for different types of d…

SBMs learn manifold-like structures by mixing samples with a non-conservative field.

In this note we prove the Weinstein conjecture for a class of symplectic manifolds including the uniruled manifolds based on Liu-Tian's result.

Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.

Establishes a link between heat diffusion and manifold distances in data.

We present a simple combinatorial method to encode 3-dimensional manifolds, based on their Heegaard diagrams. The notion of a Gauss diagram of a 3-manifold is introduced. We check the conditions for a Gauss diagram to represent a closed manifold and a manifold with boundary.

This paper is a sequel to arXiv:1108.0967. We further study Gromov-Hausdorff collapsing limits of Ricci-flat Kähler metrics on abelian fibered Calabi-Yau manifolds. Firstly, we show that in the same setup as arXiv:1108.0967, if the dimension of the base manifold is one, the limit metric space is homeomorphic to the bas…

The paper calculates curvature formulas for stable Higgs bundles.

Every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infrasolv fibers which is called its infrasolv tower. The tower arises from the solvable radicals of isometry group actions on the universal covers. Its length and the geometry of its base measure the degree of continuo…

Introduces a new manifold from a graph subgraph.

A non-linear generalization of the Dirac operator in 4-dimensions, obtained by replacing the spinor representation with a hyperKahler manifold admitting certain symmetries, is considered. We show that the existence of a covariantly constant, generalized spinor defines a Kahler structure on the base 4-dimensional manifo…

Open manifolds can be covered by $\mathbb{R}^m$ with finite or infinite degree.

MLDL preserves manifold geometry in vector transformations.

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism that canonically associates multiple independent vector bundles over a common bas…

By a classical theorem of Gallot (1979), a Riemannian cone over a complete Riemannian manifold is either flat or has irreducible holonomy. We consider metric cones with reducible holonomy over pseudo-Riemannian manifolds. First we describe the local structure of the base of the cone when the holonomy of the cone is dec…

We prove positive mass theorems on ALF manifolds, i.e. complete noncompact manifolds that are asymptotic to a circle fibration over a Euclidean base, with fibers of asymptotically constant length.

A new graph-based approach for estimating complex data with manifold structure.

We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in order to per- form non-iterative denoising directly in the graph frequency domai…

A method to fix radius distortion in generative models on curved spaces.

We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show…

A new spline method for manifold learning using Hessian-based curvature penalties.