Abstract
A surfaceM in a Riemannian manifold is said to have parallel normalized mean curvature vector if the mean curvature vector is nonzero and the unit vector in the direction of the mean curvature vector is parallel in the normal bundle. In this paper, it is proved that every analytic surface in a euclideanm-spaceEm with parallel normalized mean curvature vector must either lies in aE4 or lies in a hypersphere ofEm as a minimal surface. Moreover, it is proved that if a Riemann sphere inEm has parallel normalized mean curvature vector, then it lies either in aE3 or in a hypersphere ofEm as a minimal surfaces. Applications to the classification of surfaces with constant Gauss curvature and with parallel normalized mean curvature vector are also given.
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.
