Bearing in mind this historical context, in our present project we obtain new relationships involving intrinsic and extrinsic curvature invariants, under natural geometric conditions.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:Nash’s Theorem, any Riemannian manifold can be embedded into a Euclidean ambient space with dimension sufficiently large.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Bearing in mind this historical context, in our present project we obtain new relationships involving intrinsic and extrinsic curvature invariants, under natural geometric conditions.
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.
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Suceava, B. D.: The amalgamatic curvature and the orthocurvatures of three dimensional hypersurfaces in the Euclidean space. Publ. Math. Debrecen. 87, 35–46 (2015). DOI: 10.5486/PMD.2015.7003
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Brzycki, B., Giesler, M. D., Gomez, K., Odom, L. H., Suceav˘a, B.D.: A ladder of curvatures for hypersurfaces in the Euclidean ambient space. Houston Journal of Mathematics. 40 (4), 1347–1356 (2014).
Conley, C.T.R., Etnyre, R., Gardener, B., Odom, L.H., Suceav˘a, B. D., New curvature inequalities for hypersurfaces in the Euclidean ambient space, Taiwanese J. Math. 17 (3) 885–895 (2013). DOI: 10.11650/tjm.17.2013.2504.