Geodesic
Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$
Archivum mathematicum, Tome 36 (2000) no. 4, pp. 305-312 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The Ito equation is shown to be a geodesic flow of $L^2$ metric on the semidirect product space ${\widehat{{\it Diff}^s(S^1) \bigodot C^{\infty }(S^1)}}$, where ${\it Diff}^s(S^1)$ is the group of orientation preserving Sobolev $H^s$ diffeomorphisms of the circle. We also study a geodesic flow of a $H^1$ metric.
The Ito equation is shown to be a geodesic flow of $L^2$ metric on the semidirect product space ${\widehat{{\it Diff}^s(S^1) \bigodot C^{\infty }(S^1)}}$, where ${\it Diff}^s(S^1)$ is the group of orientation preserving Sobolev $H^s$ diffeomorphisms of the circle. We also study a geodesic flow of a $H^1$ metric.
Classification : 35Q53, 37K10, 37K65, 58D05
Keywords: Bott-Virasoro Group; Ito equation 
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Guha, Partha. Ito equation as a geodesic flow on $\widehat {\text{Diff}\sp {s}(S\sp 1) \bigodot C\sp {\infty }(S\sp 1)}$. Archivum mathematicum, Tome 36 (2000) no. 4, pp. 305-312. http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a7/

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