arXiv subjects

R. Bakhshandeh-Chamazkoti

Publications and source records attributed to R. Bakhshandeh-Chamazkoti.

2 recordsLinked to original sources

arXiv2022

Geometry of submanifolds of all classes of third-order ODEs as a Riemannian manifold

In this paper, we prove that any surface corresponding to linear second-order ODEs as a submanifold is minimal in all classes of third-order ODEs $y'''=f(x, y, p, q)$ as a Riemannian manifold where $y'=p$ and $y''=q$, if and only if $q_{yy}=0$. Moreover, we will see the linear second-order ODE with general form $y''=\pm y+β(x)$ is the only case that is defined a minimal surface and is also totally geodesic.

math.DG↗

arXiv2009

Fuzzy Lie Groups

In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a ${\cal C}^1$ fuzzy submanifold after reviewing ${\cal C}^1-$fuzzy manifold definition. In main section, we defined the Lie group and some its relative concepts such as fuzzy transformation group, fuzzy $G$-invariant. Our aim is to prepare the suitable conditions for defining fuzzy differential invariant by constructing suitable objects.

math.DG↗