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In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional Euclidean space, usually denoted by (read "two"). Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is defined for a smooth immersed submanifold in a Riemannian manifold.

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rdfs:label	Second fundamental form (en)
rdfs:comment	In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional Euclidean space, usually denoted by (read "two"). Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is defined for a smooth immersed submanifold in a Riemannian manifold. (en)
sameAs	Second fundamental form Second fundamental form
dbp:wikiPageUsesTemplate	dbt:= dbt:Cite_book dbt:Math dbt:Short_description dbt:Curvature
Subject	Curvature (mathematics) Differential geometry Differential geometry of surfaces Riemannian geometry Tensors
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Second_fundamental_form?oldid=1053959201&ns=0
Wikipage page ID	652078 (xsd:integer)
page length (characters) of wiki page	9815 (xsd:nonNegativeInteger)
Wikipage revision ID	1053959201 (xsd:integer)
has abstract	In differential geometry, the second fundamental form (or shape tensor) is a quadratic form on the tangent plane of a smooth surface in the three-dimensional Euclidean space, usually denoted by (read "two"). Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. More generally, such a quadratic form is defined for a smooth immersed submanifold in a Riemannian manifold. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Second_fundamental_form
is Wikipage redirect of	Second fundamental tensor Shape tensor
is Link from a Wikipage to another Wikipage of	Foundations of Differential Geometry Biharmonic map Bonnet theorem Canonical form Canonical quantum gravity Carathéodory conjecture Geodesic curvature Geometric calculus Gerhard Huisken Gibbons–Hawking–York boundary term Glossary of Riemannian and metric geometry David Hestenes Differential geometry Differential geometry of surfaces Chern's conjecture for hypersurfaces in spheres Curvature Curvature of Riemannian manifolds List of differential geometry topics Dupin's theorem Earth radius Darboux frame First fundamental form Gauss curvature flow Gaussian curvature Gauss–Codazzi equations Grassmann bundle Mean curvature Affine focal set

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