arXiv subjects

Abbas Heydari

Publications and source records attributed to Abbas Heydari.

6 recordsLinked to original sources

arXiv2025

\phi-Sectional curvature of statistical structures on almost contact metric manifolds

In this article, we study and analyze the \phi-sectional curvature induced by a statistical structure on an almost contact metric manifold. We demonstrate that this sectional curvature is always non-positive. Additionally, we present equivalent statements regarding the vanishing of this type of sectional curvature. Furthermore, we derive a sufficient condition for an almost contact statistical manifold to be classified as a cosymplectic statistical manifold.

math.DG↗

arXiv2024

Kähler Immersions of ALE Kähler Manifolds into Complex Space Forms

In this article, we investigate the Kähler immersions of special Asymptotically Locally Euclidean (ALE) Kähler metrics into complex space forms. We provide a relation between Kähler immersions problem of these metrics and the sign of their mass. Our result shows that these metrics with positive mass do not admit a Kähler immersion into complex Euclidean space. Moreover, we also obtain that these metrics with any sign of mass cannot be Kähler immersed into complex hyperbolic space.

math.DG↗

arXiv2022

Local and Global Structure Preservation Based Spectral Clustering

Spectral Clustering (SC) is widely used for clustering data on a nonlinear manifold. SC aims to cluster data by considering the preservation of the local neighborhood structure on the manifold data. This paper extends Spectral Clustering to Local and Global Structure Preservation Based Spectral Clustering (LGPSC) that incorporates both global structure and local neighborhood structure simultaneously. For this extension, LGPSC proposes two models to extend local structures preservation to local and global structures preservation: Spectral clustering guided Principal component analysis model and Multilevel model. Finally, we compare the experimental results of the state-of-the-art methods with our two models of LGPSC on various data sets such that the experimental results confirm the effectiveness of our LGPSC models to cluster nonlinear data.

cs.LG↗

arXiv2016

On contact and symplectic Lie algebroids

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by means of the induced Poisson structures on the integral submanifolds. Moreover, for any compatible triple with invariant metric and admissible almost complex structure, we show that the bracket annihilates on the kernel of the anchor map.

math.DG↗

arXiv2015

Decomposition of Euclidean Nearly Kähler submanifolds

We study the foliation space of complex and invariant (by torsion of intrinsic Hermitian connection) umbilic distribution on an isometric immersion from a nearly Kähler manifold $M$ into the Euclidean space. Under suitable conditions this leaf space is nearly Kähler and $M$ can be decomposed into a product of this leaf space and a 6-dimensional locally homogeneous nearly Kähler manifold.

math.DG↗

arXiv2014

Nearly Kähler submanifolds of a space form

In this article we study isometric immersions of nearly Kähler manifolds into a space form (specially Euclidean space) and show that every nearly Kähler submanifold of a space form has a totally umbilic foliation whose leafs are 6-dimensional nearly Kähler manifolds. Moreover using this foliation we show that there is no non-homogeneous 6-dimensional nearly Kähler submanifold of a space form. We prove some results towards a classification of nearly Kähler hypersurfaces in standard space forms.

math.DG↗