adjective বিশেষণ পদ

Riemannian meaning in assamese


  • Definition

    of or relating to Riemann's non-Euclidean geometry

    ৰিমেনৰ অ-ইউক্লিডীয় জ্যামিতিৰ বা ইয়াৰ সৈতে জড়িত

adjective বিশেষণ পদ

Riemannian meaning in assamese


  • Definitions

    1. Of or relating to the work, or theory developed from the work, of German mathematician Bernhard Riemann, especially to Riemannian manifolds and Riemannian geometry.

    জাৰ্মান গণিতজ্ঞ বাৰ্নহাৰ্ড ৰিমেনৰ কামৰ বা কামৰ পৰা বিকশিত হোৱা তত্ত্বৰ বিষয়ে বা ইয়াৰ সৈতে জড়িত, বিশেষকৈ ৰিমেনিয়ান মেনিফল্ড আৰু ৰিমেনিয়ান জ্যামিতিৰ সৈতে।

  • Examples:
    1. 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 g ¯ = d t 2 + t 2 g {\displaystyle {\overline {g}}=dt^{2}+t^{2}g} together with the symplectic form ω {\displaystyle \omega } into a Kähler manifold. Then g ¯ {\displaystyle {\overline {g}}} and ω {\displaystyle \omega } define a complex structure Φ ¯ {\displaystyle {\overline {\Phi }}} . Alternatively, one could ask for a Riemannian metric g {\displaystyle g} on M {\displaystyle M} which would define a Kähler metric h {\displaystyle h} on Z {\displaystyle {\mathcal {Z}}} via a Riemannian submersion.

    2. 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)}$V$A ^ ( M ) = det ( R / 2 sinh ⁡ ( R / 2 ) ) {\displaystyle {\hat {A}}(M)={\sqrt {\operatorname {det} }}\left({\frac {R/2}{\sinh(R/2)}}\right)}$V$A ^ ( M ) = det ( R / 2 sinh ⁡ ( R / 2 ) ) {\displaystyle {\hat {A}}(M)={\sqrt {\operatorname {det} }}\left({\frac {R/2}{\sinh(R/2)}}\right)}$V$A ^ ( M ) = det ( R / 2 sinh ⁡ ( R / 2 ) ) {\displaystyle {\hat {A}}(M)={\sqrt {\operatorname {det} }}\left({\frac {R/2}{\sinh(R/2)}}\right)}$V$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.

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

  • 2. Relating to the musical theories of German theorist Hugo Riemann, particularly his theory of harmony, which is characterised by a system of "harmonic dualism".

    জাৰ্মান তত্ত্ববিদ হুগো ৰিমেনৰ সংগীত তত্ত্বৰ সৈতে জড়িত, বিশেষকৈ তেওঁৰ সমন্বয় তত্ত্ব, যিটো "হাৰমনিক দ্বৈতবাদ"ৰ ব্যৱস্থাৰ দ্বাৰা চিহ্নিত।

  • Examples:
    1. And not only theory: most central European composers of this century were schooled in Riemannian doctrine of one type or another.

    2. 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.

    3. 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.

  • Synonyms

    Riemannian geometry (ৰিমেনিয়ান জ্যামিতি)

    pseudo-Riemannian (ছ্যুডো-ৰিমেনিয়ান)

    neo-Riemannian (নব্য-ৰিমেনিয়ান)

    Riemannian manifold (ৰিমেনিয়ান মেনিফল্ড)