INFINITESIMAL DERIVATIVE OF THE BOTT CLASS AND THE SCHWARZIAN DERIVATIVES

An infinitesimal derivative of the Bott class is defined by generalizing Heitsch’es construction. We prove a formula relating the infinitesimal derivative to the Schwarzian derivatives, which gives a generalization of the Maszczyk formula for the Godbillon-Vey class of real codimensionone foliations. As an application, a residue of infinitesimal derivatives with respect to the Julia set in the sense of Ghys, Gomez-Mont and Saludes is introduced.

[1]  M. Crampin,et al.  On projective connections: the ane case , 2004 .

[2]  Fumio Kikuchi,et al.  Remarks on a posteriori error estimation for finite element solutions , 2007 .

[3]  R. Bott,et al.  Lectures on Algebraic and Differential Topology , 1972 .

[4]  Raoul Bott,et al.  Lectures on characteristic classes and foliations , 1972 .

[5]  J. Noguchi,et al.  Degeneracy of holomorphic curves into algebraic varieties , 2005, math/0507122.

[6]  Hirotaka Fushiya.  Limit theorem of a one dimensional Marokov process to sticky reflected Brownian motion , 2005 .

[7]  T. Asuke.  Godbillon-Vey Class of Transversely Holomorphic Foliations , 2010 .

[8]  J. Heitsch.  Independent variation of secondary classes , 1978 .

[9]  Ken-Ichi Yoshikawa.  On the singularity of Quillen metrics , 2006 .

[10]  J. Heitsch.  A cohomology for foliated manifolds , 1973 .

[11]  J. Heitsch.  Derivatives of secondary characteristic classes , 1978 .

[12]  Jin Cheng,et al.  The conditional stability in line unique continuation for a wave equation and an inverse wave source problem , 2005 .

[13]  Serge Tabachnikov,et al.  Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups , 2004 .

[14]  Masahiro Yamamoto,et al.  A stability result via Carleman estimates for an inverse source problem related to a hyperbolic integro-differential equation , 2006 .

[15]  C. Benson,et al.  Characteristic classes of transversely homogeneous foliations , 1985 .

[16]  Hao Fang,et al.  ANALYTIC TORSION FOR CALABI-YAU THREEFOLDS , 2006 .

[17]  S. Saitoh,et al.  Some stability estimates in determining sources and coefficients , 2005 .

[18]  S. Morita,et al.  Invariant polynomials of the automorphism group of a compact complex manifold , 1985 .

[19]  T. Duchamp,et al.  Deformation theory for holomorphic foliations , 1979 .

[20]  Ken-Ichi Yoshikawa.  Real K3 surfaces without real points, equivariant determinant of the Laplacian, and the Borcherds Φ-function , 2006 .

[21]  A. Futaki.  On a character of the automorphism group of a compact complex manifold , 1987 .

[22]  Yuuki Tadokoro,et al.  A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic , 2005, math/0508433.