## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Strong symplectic structures on spaces of probability measures with positive density function

Yuichi Shishido

#### Abstract

Spaces of probability measures with positive density function on a compact Riemannian manifold are endowed with a closed 2-form associated with the Fisher information metric by using a divergence-free vector field. In this note we give a necessary and sufficient condition on the vector field that this 2-form is a strong symplectic structure.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 7 (2005), 134-136.

Dates
First available in Project Euclid: 3 October 2005

https://projecteuclid.org/euclid.pja/1128346018

Digital Object Identifier
doi:10.3792/pjaa.81.134

Mathematical Reviews number (MathSciNet)
MR2172604

Zentralblatt MATH identifier
1095.53054

Subjects
Primary: 53D05: Symplectic manifolds, general

#### Citation

Shishido, Yuichi. Strong symplectic structures on spaces of probability measures with positive density function. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 7, 134--136. doi:10.3792/pjaa.81.134. https://projecteuclid.org/euclid.pja/1128346018

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