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

Authors : Bogdan Suceava, Anh Du Tran

Pages : 146-152

Doi:10.36890/iejg.1366352

View : 80 | Download : 104

Publication Date : 2024-04-23

Article Type : Research Paper

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