Abstract
In this paper, we construct a helicoidal surface with a prescribed weighted mean curvature and weighted extrinsic curvature in a 3-dimensional complete manifold with a positive density function. We get a result for the minimal case. Additionally, we give examples of a helicoidal surface with a weighted mean curvature and weighted extrinsic curvature.
Highlights
It is well known that a helicoidal surface is a generalization of a rotation surface
Lee et al studied the helicoidal surfaces with a prescribed extrinsic curvature or mean curvature in a conformally flat 3-space [10]
We study helicoidal surfaces in a 3-dimensional complete manifold with density
Summary
It is well known that a helicoidal surface is a generalization of a rotation surface. Baikoussis et al studied helicoidal surfaces with a prescribed mean and Gaussian curvature in R3 [13]. For more details on manifolds with density and surfaces in manifold with density, see References [18,19,20,21,22,23,24,25] This problem is extended to complete manifolds. Lee et al studied the helicoidal surfaces with a prescribed extrinsic curvature or mean curvature in a conformally flat 3-space [10]. For a given surface in a complete manifold with a conformal factor function F, the mean curvature and the extrinsic curvature are given by: HgF = FHg0 − hN, grad F i ,. We construct a helicoidal surface with a prescribed weighted mean and weighted extrinsic curvature.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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.
