Riemannian
التعريفات والمعاني
== English ==
=== Etymology ===
From Riemann + -ian.
=== Adjective ===
Riemannian (not comparable)
(mathematics) Of or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry.
2003, Maung Min-Oo, The Dirac Operator in Geometry and Physics, Steen Markvorsen, Maung Min-Oo (editors), Global Riemannian Geometry: Curvature and Topology, Springer, page 62,
Similarly,
A
^
(
M
)
{\displaystyle {\hat {A}}(M)}
is represented by the closed differential form
A
^
(
M
)
=
det
(
R
/
2
sinh
(
R
/
2
)
)
{\displaystyle {\hat {A}}(M)={\sqrt {\operatorname {det} }}\left({\frac {R/2}{\sinh(R/2)}}\right)}
where
R
{\displaystyle R}
is the Riemannian curvature of the metric
g
{\displaystyle g}
, regarded as an
End
(
T
M
)
{\displaystyle \textstyle \operatorname {End} (TM)}
-valued two form, and
det
{\displaystyle {\sqrt {\operatorname {det} }}}
is the Pfaffian, which is an invariant polynomial defined on the Lie algebra of skew symmetric matrices in even dimensions.
2012, Yves Carriere, Appendix A: Variations on Riemannian Flows, Pierre Molino, Riemannian Foliations, Springer, page 217,
The object of this appendix is to give a summary of known results on 1-dimensional oriented Riemannian Foliations.
(music) Relating to the musical theories of German theorist Hugo Riemann, particularly his theory of harmony, which is characterised by a system of "harmonic dualism".
==== Derived terms ====
neo-Riemannian
pseudo-Riemannian
Riemannian geometry
Riemannian manifold
==== Translations ====
=== Noun ===
Riemannian (plural Riemannians)
(mathematics) One who uses or supports the work of German mathematician Bernhard Riemann.
==== Translations ====
=== See also ===
Riemann
Riemann integral
=== Further reading ===
(mathematics):
Bernhard Riemann on Wikipedia.Wikipedia
Riemannian geometry on Wikipedia.Wikipedia
Riemannian manifold on Wikipedia.Wikipedia
(music):
Riemannian theory on Wikipedia.Wikipedia
Neo-Riemannian theory on Wikipedia.Wikipedia
Tonnetz on Wikipedia.Wikipedia