# Riemannian

suomi-englanti sanakirja## Riemannian englannista suomeksi

Riemannin

#### Substantiivi

## Riemannian englanniksi

Of or relating to the work, or theory developed from the work, of German mathematician

*(w)*, especially to manifolds and 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, \hat A(M) is represented by the closed differential form
- ::: \hat A(M) = \sqrt{\operatorname{det\left (\frac{R/2}{\sinh(R/2)} \right )
- where R is the Riemannian curvature of the metric g, regarded as an \textstyle\operatorname{End}(TM)-valued two form, and \sqrt{\operatorname{det is the Pfaffian, which is an invariant polynomial defined on the Lie algebra of skew symmetric matrices in even dimensions.
2010, Charles P. Boyer, Krzysztof Galicki, ''Chapter 3: Sasakian geometry, holonomy, and supersymmetry'', Vicente Cortés (editor), ''Handbook of Pseudo-Riemannian Geometry and Supersymmetry'',

*(w)*, page 41,- As the preferred metrics applied to symplectic forms are Kähler metrics one could ask for the Riemannian structure which would make the cone with the metric \overline g = dt^2 + t^2g together with the symplectic form \omega into a Kähler manifold. Then \overline g and \omega define a complex structure \overline \Phi. Alternatively, one could ask for a Riemannian metric g on M which would define a Kähler metric h on \mathcal Z via a Riemannian submersion.
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.
Relating to the musical theories of German theorist

*(w)*, particularly his theory of harmony, which is characterised by a system of "harmonic dualism".1994, Daniel Harrison, ''Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents'',

*(w)*, page 7,- And not only theory: most central European composers of this century were schooled in Riemannian doctrine of one type or another.
2004, Jairo Moreno, ''Musical Representations, Subjects, and Objects: The Construction of Musical Thought in Zarlino, Descartes, Rameau, and Weber'',

*(w)*, page 1,- Or take, for example, the rehabilitation by late-twentieth-century North American theorists of Riemannian ''Tonnetze'' as a means to navigate the voice-leading intricacies of much chromatic and post-chromatic music.
2009, Marek Žabka, ''Generalized Tonnetz and Well-Formed GTS: A Scale Theory Inspired by the Neo-Riemannians'', Elaine Chew, Adrian Childs, Ching-Hua Chuan (editors), ''Mathematics and Computation in Music, 2nd International Conference, Proceedings'', Springer, page 286,

- The paper connects two notions originating from different branches of the recent mathematical music theory: the neo-Riemannian ''
*(w)*'' and the property of well-formedness from the theory of the generated scales. One who uses or supports the work of German mathematician

*(w)*.