Tohoku Mathematical Journal
2017

March
SECOND SERIES VOL. 69, NO. 1

Tohoku Math. J.
69 (2017), 129-139

Title NOTES ON `INFINITESIMAL DERIVATIVE OF THE BOTT CLASS AND THE SCHWARZIAN DERIVATIVES'

Author Taro Asuke

(Received December 18, 2014)
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.

Mathematics Subject Classification. Primary 58H10; Secondary 32S65, 53B10, 58H15, 53C12, 53C15.

Key words and phrases. Foliations, characteristic classes, deformations.

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