Abstract
By J.F. Nash’s Theorem, any Riemannian manifold can be embedded into a Euclidean ambient space with dimension sufficiently large. In 1968, S.-S. Chern pointed out that a key technical element in applying Nash’s Theorem effectively is finding useful relationships between intrinsic and extrinsic elements that are characterizing immersions. After 1993, when a groundbreaking work written by B.-Y. Chen on this theme was published, many explorations pursued this important avenue of inquiry. Bearing in mind this historical context, in our present paper we point out a new relationship involving intrinsic and extrinsic curvature invariants, under natural geometric conditions. We conclude our work with an obstruction to minimality, in the spirit of S.-S. Chern’s reflection from 1968.
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 callMore From: Annals of the Alexandru Ioan Cuza University - Mathematics
Disclaimer: 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.
