B.-Y. Chen-Type Inequalities for Three Dimensional Smooth Hypersurfaces

Year 2024, Volume: 17 Issue: 1, 146 - 152, 23.04.2024

Bogdan Suceava Anh Du Tran

https://doi.org/10.36890/iejg.1366352

Abstract

By J.F. Nash’s Theorem, any Riemannian manifold can be embedded into a Euclidean ambient
space with dimension sufficiently large. S.-S. Chern pointed out in 1968 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. Bearing in mind this historical context, in our present project we obtain
new relationships involving intrinsic and extrinsic curvature invariants, under natural geometric
conditions.

Keywords

Principal curvatures, smooth surfaces, smooth hypersurfaces

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