## Tohoku Mathematical Journal

### Notes on 'Infinitesimal derivative of the Bott class and the Schwarzian derivatives'

Taro Asuke

#### Abstract

The derivatives of the Bott class and those of the Godbillon-Vey class with respect to infinitesimal deformations of foliations, called infinitesimal derivatives, are known to be represented by a formula in the projective Schwarzian derivatives of holonomies [3], [1]. It is recently shown that these infinitesimal derivatives are represented by means of coefficients of transverse Thomas-Whitehead projective connections [2]. We will show that the formula can be also deduced from the latter representation.

#### Article information

Source
Tohoku Math. J. (2), Volume 69, Number 1 (2017), 129-139.

Dates
First available in Project Euclid: 26 April 2017

https://projecteuclid.org/euclid.tmj/1493172132

Digital Object Identifier
doi:10.2748/tmj/1493172132

Mathematical Reviews number (MathSciNet)
MR3640018

Zentralblatt MATH identifier
06726845

#### Citation

Asuke, Taro. Notes on 'Infinitesimal derivative of the Bott class and the Schwarzian derivatives'. Tohoku Math. J. (2) 69 (2017), no. 1, 129--139. doi:10.2748/tmj/1493172132. https://projecteuclid.org/euclid.tmj/1493172132

#### References

• T. Asuke, Infinitesimal derivative of the Bott class and the Schwarzian derivatives, Tohoku Math. J. (2) 61 (2009), 393–416.
• T. Asuke, Transverse projective structures of foliations and infinitesimal derivatives of the Godbillon-Vey class, Internat. J. Math. 26 (2015), 1540001, 29pp.
• T. Maszczyk, Foliations with rigid Godbillon-Vey class, Math. Z. 230 (1999), 329–344.
• T. Mizutani, The Godbillon-Vey cocycle of $\mathrm{Diff} \mathbb{R}^n$, A fête of Topology: papers dedicated to Itiro Tamura, pp. 49–62, Academic Press, Boston, MA, 1988.