Last Updated：2025/11/29
(mathematics) One aspect of the study of differential forms of a smooth manifold M. More specifically, it works out the consequences for the cohomology groups of M, with real coefficients, of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M.
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Hodge theory
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Source Word
Hodge theory
Noun
uncountable
(mathematics)
One
aspect
of
the
study
of
differential
forms
of
a
smooth
manifold
M.
More
specifically,
it
works
out
the
consequences
for
the
cohomology
groups
of
M,
with
real
coefficients,
of
the
partial
differential
equation
theory
of
generalised
Laplacian
operators
associated
to
a
Riemannian
metric
on
M.
Japanese Meaning
数学における理論の一分野で、滑らかな多様体上の微分形式の研究を通して、リーマン計量に関連付けられた一般化されたラプラス演算子の偏微分方程式理論が実係数を持つコホモロジー群にどのような影響を与えるかを明らかにするもの
Sense（1）
(mathematics)
One
aspect
of
the
study
of
differential
forms
of
a
smooth
manifold
M.
More
specifically,
it
works
out
the
consequences
for
the
cohomology
groups
of
M,
with
real
coefficients,
of
the
partial
differential
equation
theory
of
generalised
Laplacian
operators
associated
to
a
Riemannian
metric
on
M.
