Nonholonomic Frame for a Deformed  (α,β)(α,β)(\alpha,\beta )-metric

Laurian-loan PISCORAN

doi:https://doi.org/10.36890/iejg.973879

Article Details

Nonholonomic Frame for a Deformed (α,β)(α,β)(\alpha,\beta )-metric

Authors:

Laurian-loan PISCORAN

Publisher:

Kazım İLARSLAN

Main Topics:

Mathematics

Journal:

International Electronic Journal of Geometry 2021 Vol.14 Issue 2, pp.231-238

Document Type:

Article

Publication Date:

10/2021

Document Language:

English

Document ID (Org No.):

2000471514

Frequency:

Bi-Annual

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.973879

Abstract:

 

Recently, in paper [14], we have introduced the following deformed (α,β)(α,β)(\alpha, \beta)-metric:  Fϵ(α,β)=β2+α2(a+1)α+ϵβFϵ(α,β)=β2+α2(a+1)α+ϵβ 	F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta 		 where α=√aijyiyjα=aijyiyj\alpha=\sqrt{a_{ij}y^{i}y^{j}} is a Riemannian metric; β=biyiβ=biyi\beta=b_{i}y^{i} is a 1-form, |ϵ|<2√a+1|ϵ|<2a+1\left|\epsilon\right|<2\sqrt{a+1} is a real parameter and a∈(14,+∞)a∈(14,+∞)a\in \left(\frac{1}{4},+\infty\right) is a real positive scalar. 	The aim of this paper is to find the nonholonomic frame for this important kind of (α,β)(α,β)(\alpha, \beta)-metric and also to investigate the Frobenius norm for the Hessian generated by this kind of metric.

Article Details

Nonholonomic Frame for a Deformed (α,β)(α,β)(\alpha,\beta )-metric

Authors: Laurian-loan PISCORAN

Publisher: Kazım İLARSLAN

Main Topics: Mathematics

Journal: International Electronic Journal of Geometry 2021 Vol.14 Issue 2, pp.231-238

Document Type: Article

Publication Date: 10/2021

Document Language: English

Document ID (Org No.): 2000471514

Frequency: Bi-Annual

eISSN: 1307-5624

DOI: https://doi.org/10.36890/iejg.973879

Issues

Authors:

Laurian-loan PISCORAN

Publisher:

Kazım İLARSLAN

Main Topics:

Mathematics

Journal:

International Electronic Journal of Geometry 2021 Vol.14 Issue 2, pp.231-238

Document Type:

Article

Publication Date:

10/2021

Document Language:

English

Document ID (Org No.):

2000471514

Frequency:

Bi-Annual

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.973879