Last Updated：2025/11/22
Sentence
微分幾何学では、正則なパラメータ表示 x(u,v) を持つ曲面の第一基本形式（曲面のリーマン計量）は、局所的な内的曲率を決定する E(u,v)、F(u,v)、G(u,v) の三つの関数によって与えられます。
Quizzes for review
In differential geometry, the first fundamental form of a surface with a regular parametrization x(u,v) is the Riemannian metric given by three functions E(u,v), F(u,v), and G(u,v) that determine the surface's local intrinsic curvature.
See correct answer
In differential geometry, the first fundamental form of a surface with a regular parametrization x(u,v) is the Riemannian metric given by three functions E(u,v), F(u,v), and G(u,v) that determine the surface's local intrinsic curvature.
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Related words
first fundamental form
Noun
uncountable
(differential
geometry)
the
Riemannian
metric
for
2-dimensional
manifolds,
i.e.
given
a
surface
with
regular
parametrization
x(u,v),
the
first
fundamental
form
is
a
set
of
three
functions,
{E,
F,
G},
dependent
on
u
and
v,
which
give
information
about
local
intrinsic
curvature
of
the
surface.
These
functions
are
given
by
Japanese Meaning
微分幾何学において、曲面の局所的な内部曲率や計量情報を与えるリーマン計量の一形態。具体的には、正則なパラメトリゼーション x(u,v) を持つ曲面に対して、3つの関数 {E, F, G} により構成され、局所的な計量（第一基本形式）として扱われる。
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