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.
Primary Language | English |
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Subjects | Algebraic and Differential Geometry |
Journal Section | Research Article |
Authors | |
Early Pub Date | April 6, 2024 |
Publication Date | April 23, 2024 |
Acceptance Date | December 27, 2023 |
Published in Issue | Year 2024 Volume: 17 Issue: 1 |