Source Word
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。
Sense（1）
(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
