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

Author(s):

Zeynab Bakhshandeh-Chamazkoti , Abolfazl Behzadi , Rohollah Bakhshandeh-Chamazkoti * , Mehdi Rafie-Rad

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
‎In this paper‎, ‎we prove that any surface corresponding to linear second-order ODEs‎ ‎as a submanifold is minimal in the class 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 $y''=\pm y+\beta(x)$ is the only case that is defined a minimal surface‎ ‎and is also totally geodesic‎.
Keywords:

Levi-Civita connection‎ , ‎minimal surface‎ , ‎moving frame‎ , ‎Riemannian manifold‎ , ‎Riemann curvature tensor‎ , ‎totally geodesic

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 1, Jan 2023
Pages:
1283 to 1294
https://www.magiran.com/p2563242  
سامانه نویسندگان
  • Rafie Rad، Mehdi
    Author (4)
    Rafie Rad, Mehdi
    Associate Professor Department of Mathematics, University of Mazandaran, بابلسر, Iran
اطلاعات نویسنده(گان) توسط ایشان ثبت و تکمیل شده‌است. برای مشاهده مشخصات و فهرست همه مطالب، صفحه رزومه را ببینید.
مقالات دیگری از این نویسنده (گان)