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Second fundamental form
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
hypersurface
in a
Riemannian manifold
and a smooth choice of the unit normal vector at each point.
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