MDPI - Publisher of Open Access Journals

24 pages, 335 KB

Open AccessArticle

Para-Holomorphic Statistical Structure with Cheeger Gromoll Metric

by Esmaeil Peyghan, Leila Nourmohammadifar and Ion Mihai

Mathematics 2025, 13(11), 1735; https://doi.org/10.3390/math13111735 - 24 May 2025

Viewed by 698

We consider the family of

λ

connections

\nabla^{(λ)}

on a statistical manifold M equipped with a pair of conjugate connections

\nabla = \nabla^{(1)}

and

\nabla^{*} = \nabla^{(- 1)}

, where the

λ

connection [...] Read more.

We consider the family of

λ

connections

\nabla^{(λ)}

on a statistical manifold M equipped with a pair of conjugate connections

\nabla = \nabla^{(1)}

and

\nabla^{*} = \nabla^{(- 1)}

, where the

λ

connection is defined as

\nabla^{(λ)} = \frac{1 + λ}{2} \nabla + \frac{1 - λ}{2} \nabla^{*}

. This paper develops expressions for the vertical and horizontal distributions on the tangent bundle of the statistical manifold

(M, g, \nabla^{(λ)})

and introduces the concept of

λ

-adapted frames. We also derive the Levi–Civita connection

{}^{C G}{\hat{\nabla}}^{(λ)}

of the tangent bundle

T M

, which is equipped with the Cheeger Gromoll-type metric

{}^{C G}g

. We study the statistical structure

({}^{C G}g, {{}^{C G}\nabla}^{(λ)})

on the tangent bundle

T M

, which is naturally induced from the statistical manifold

(M, g, \nabla^{(λ)})

. By introducing a para-holomorphic structure on the statistical manifold

(M, g, \nabla^{(λ)})

, we construct a para-Hermitian structure on the tangent bundle

T M

and examine its integrability. Finally, we present the conditions under which these bundles admit a para-holomorphic structure. Full article

(This article belongs to the Section B: Geometry and Topology)

3 pages, 158 KB

Open AccessCorrection

Correction: Alegre, P.; Carriazo, A. Bi-Slant Submanifolds of Para Hermitian Manifolds. Mathematics 2019, 7, 618

by Pablo Alegre and Alfonso Carriazo

Mathematics 2025, 13(7), 1170; https://doi.org/10.3390/math13071170 - 2 Apr 2025

Viewed by 388

Abstract

In the published publication [...] Full article

34 pages, 558 KB

Open AccessArticle

D-Branes in Para-Hermitian Geometries

by Vincenzo Emilio Marotta and Richard J. Szabo

Universe 2022, 8(4), 200; https://doi.org/10.3390/universe8040200 - 23 Mar 2022

Cited by 6 | Viewed by 2111

Abstract

We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string version of the Born sigma-model, where they are given by maximally isotropic vector bundles which do not generally admit the standard geometric picture in terms of submanifolds. When reduced to the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold, integrable branes yield D-branes as leaves of foliations which are interpreted as Dirac structures on the physical spacetime. We define a notion of generalised para-complex D-brane, which realises our D-branes as para-complex versions of topological A/B-branes. We illustrate how our formalism recovers standard D-branes in the explicit example of reductions from doubled nilmanifolds. Full article

(This article belongs to the Special Issue Dualities and Geometry)

15 pages, 284 KB

Open AccessFeature PaperArticle

Bi-Slant Submanifolds of Para Hermitian Manifolds

by Pablo Alegre and Alfonso Carriazo

Mathematics 2019, 7(7), 618; https://doi.org/10.3390/math7070618 - 11 Jul 2019

Cited by 19 | Viewed by 3324 | Correction

Abstract

In this paper, we introduce the notion of bi-slant submanifolds of a para Hermitian manifold. They naturally englobe CR, semi-slant, and hemi-slant submanifolds. We study their first properties and present a whole gallery of examples. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

Search Results (4)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (4)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI