riemannian

Adjective

Adjective

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Adjective

**riemannian** (*not comparable*)

- Alternative letter-case form of
*Riemannian#English|Riemannian*

**Riemannian**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*, Springer, page 62 ↗,**Riemannian**Geometry: Curvature and Topology- 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.

- Similarly, \hat A(M) is represented by the closed differential form
**2010**, Charles P. Boyer, Krzysztof Galicki,*Chapter 3: Sasakian geometry, holonomy, and supersymmetry*, Vicente Cortés (editor),*Handbook of Pseudo-*, European Mathematical Society, page 41 ↗,**Riemannian**Geometry and Supersymmetry- 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.

- As the preferred metrics applied to symplectic forms are Kähler metrics one could ask for the
**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.

- The object of this appendix is to give a summary of known results on 1-dimensional oriented

- (
*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".**1994**, Daniel Harrison,*Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents*, University of Chicago Press, page 7 ↗,- And not only theory: most central European composers of this century were schooled in
**Riemannian**doctrine of one type or another.

- And not only theory: most central European composers of this century were schooled in
**2004**, Jairo Moreno,*Musical Representations, Subjects, and Objects: The Construction of Musical Thought in Zarlino, Descartes, Rameau, and Weber*, Indiana University Press, 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.

- Or take, for example, the rehabilitation by late-twentieth-century North American theorists of
**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***Tonnetz*and the property of well-formedness from the theory of the generated scales.

- The paper connects two notions originating from different branches of the recent mathematical music theory: the neo-

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