We present a new proof, as well as a C/Q extension, of the RiemannRoch-Grothendieck theorem of Bismut-Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of ηinvariants associated to the so-called sub-signature operators. We further show that the Bismut-Lott analytic torsion form can be derived naturally from the transgression of the η-forms appea...

is a module over the ring of all modular forms with respect to the group Γ2[4, 8]. We are interested in its structure. By Igusa, the ring of modular forms is generated by the ten classical theta constants θ[m]. The module M contains a submodule N which is generated by 45 Cohen-Rankin brackets {θ[m], θ[n]}. We determine defining relations for this submodule and compute its Hilbert function (Theo...

An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vectorvalued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and in CR geometry. 1 Preliminaries 1.

Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of divergence-free vector fields, which obey a particular set of chiral equations. Upon imposing the Jacobi identity upon these vector fields, we reproduce a pre...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

We prove that Schur polynomials in Chern forms of Nakano and dual positive vector bundles are as differential forms. Moreover, modulo a statement about the positivity “double mixed discriminant” linear operators on matrices, which preserve cone definite we establish Griffiths weakly This provides differential-geometric versions Fulton–Lazarsfeld inequalities for ample bundles. An interpretation...