## Tohoku Mathematical Journal

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

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

#### 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

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.2748/tmj/1493172132

**Mathematical Reviews number (MathSciNet)**

MR3640018

**Zentralblatt MATH identifier**

06726845

**Subjects**

Primary: 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]

Secondary: 32S65: Singularities of holomorphic vector fields and foliations 53B10: Projective connections 58H15: Deformations of structures [See also 32Gxx, 58J10] 53C12: Foliations (differential geometric aspects) [See also 57R30, 57R32] 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

**Keywords**

Foliations characteristic classes deformations

#### 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