Abstract
Abstract.Making use of 1-forms and geometric inequalities we prove the rigidity property of complete submanifolds Mn with parallel mean curvature normal in a complete and simply connected Riemannian (n+p) -manifold Nn+p with positive sectional curvature. For given integers n, p and for a nonnegative constant H we find a positive number T(n,p) ∈ (0,1) with the property that if the sectional curvature of N is pinched in [T(n,p), 1], and if the squared norm of the second fundamental form is in a certain interval, then Nn+p is isometric to the standard unit (n + p)-sphere. As a consequence, such an M is congruent to one of the five models as seen in our Main Theorem.
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.
