Abstract
We consider a new kind of helicoidal surface for natural numbers ( m , n ) in the three-dimensional Euclidean space. We study a helicoidal surface of value ( m , n ) , which is locally isometric to a rotational surface of value ( m , n ) . In addition, we calculate the Laplace–Beltrami operator of the rotational surface of value ( 0 , 1 ) .
Highlights
The notion of the finite-type immersion of submanifolds of a Euclidean space has been used in classifying and characterizing well-known Riemannian submanifolds [1]
Chen posed the problem of classifying the finite-type surfaces in the three-dimensional Euclidean space E3
The theory of submanifolds of a finite type was studied by many geometers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
Summary
The notion of the finite-type immersion of submanifolds of a Euclidean space has been used in classifying and characterizing well-known Riemannian submanifolds [1]. Rotational) surface that is minimal in classical surface geometry in Euclidean space. The French mathematician Edmond Bour used the semi-geodesic coordinates and found a number of new cases of the deformation of surfaces in 1862 He gave in [25] a well-known theorem about the helicoidal and rotational surfaces. Güler [28] studied the isometric helicoidal and rotational surfaces of value m. We consider a new kind of helicoidal surface of value (m, n) in Euclidean three-space E3 in this paper.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
