A fundamental inequality for 3-dimensional CAT(ε) hypersurfaces
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 eleme...
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| Veröffentlicht in: | Analele ştiinţifice ale Universitatii "Al. I. Cuza" din Iaşi. Secţiunea 1a: Matematicǎ 2024, Vol.70 (1), p.83-87 |
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| container_title | Analele ştiinţifice ale Universitatii "Al. I. Cuza" din Iaşi. Secţiunea 1a: Matematicǎ |
| container_volume | 70 |
| creator | Suceavă, Bogdan D. |
| description | 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. |
| doi_str_mv | 10.47743/anstim.2024.00006 |
| format | Article |
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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
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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
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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
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| ispartof | Analele ştiinţifice ale Universitatii "Al. I. Cuza" din Iaşi. Secţiunea 1a: Matematicǎ, 2024, Vol.70 (1), p.83-87 |
| issn | 1221-8421 2344-4967 |
| language | eng |
| recordid | cdi_crossref_primary_10_47743_anstim_2024_00006 |
| source | EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection |
| title | A fundamental inequality for 3-dimensional CAT(ε) hypersurfaces |
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