Geometry

2302 Submissions

[2] viXra:2302.0127 [pdf] submitted on 2023-02-23 02:17:18

Semi-Stable Quiver Bundles Over Gauduchon Manifolds

Authors: Dan-Ni Chen, Jing Cheng, Xiao Shen, Pan Zhang
Comments: 12 Pages.

In this paper, we prove the existence of the approximate $(sigma,tau)$-Hermitian Yang--Mills structure on the $(sigma,tau)$-semi-stable quiver bundle $mathcal{R}=(mathcal{E},phi)$ over compact Gauduchon manifolds. An interesting aspect of this work is that the argument on the weakly $L^{2}_1$-subbundles is different from ['{A}lvarez-C'{o}nsul and Garc'{i}a-Prada, Comm Math Phys, 2003] and [Hu--Huang, J Geom Anal, 2020].
Category: Geometry

[1] viXra:2302.0117 [pdf] submitted on 2023-02-22 04:24:29

Two Notes on Regular Polygons: Geometric Motivation of the π Constant

Authors: Irakli Dochviri, Ana Chokhonelidze
Comments: 3 Pages.

In the paper we prove that the ratio between the circumference of the incircle of the regularn-gon and its perimeter is equivalent to the ratio of their areas, respectively. These ratios are constantsfor regular n-gons. Also, it is shown that the ratio of circumference of the excircle and perimeter ofthe regular n-gon is not the same as the ratio of areas of the excircle and this regular n-gon.
Category: Geometry