The present paper is the first in a series of papers, in which we shall construct modular functors and Topological Quantum Field Theories from the conformal field theory developed in [TUY]. The basic idea is that the covariant constant sections of the sheaf of vacua associated to a simple Lie algebra over Teichmüller space of an oriented pointed surface gives the vector space the modular functo...

On an almost Hermitian manifold, there are two scalar curvatures associated with a canonical connection. In this paper, explicit formulas on these obtained in terms of the Riemannian curvature, norms components covariant derivative fundamental 2-form respect to Levi-Civita connection, and codifferential Lee form. Then we use them get characterization results Kähler metric, balanced locally conf...

We describe an algebra of meromorphic functions on the Siegel domain genus two which contains modular forms for arithmetic index six subgroup symplectic group, is closed under three canonical derivations domain. The main ingredients our study are moduli enhanced curves, Gauss-Manin connection and vector fields living such spaces.

Abstract Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue within “connection-dynamics” where one can work, throughout, only with real variables. The resulting quantum theory would then be free of complicated...

We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices differential forms. The forms are elements the middle dimensional cohomology whose variation is described by a mixed Hodge structures which equipped flat Gauss-Manin connection. construct graded rings special functions on these and show that they contain quasi-modular algebra derivations can be obtained fro...

We construct a classification of coherent sheaves with an integrable log connection, or, more precisely, sheaves with an integrable connection on a smooth log analytic space X over C. We do this in three contexts: sheaves and connections which are equivariant with respect to a torus action, germs of holomorphic connections, and finally global log analytic spaces. In each case, we construct an e...

On a Finsler manifold (M,L), we consider the change L −→ L(x, y) = eL(x, y) + β(x, y), which we call a β-conformal change. This change generalizes various types of changes in Finsler geometry: conformal, C-conformal, h-conformal, Randers and generalized Randers changes. Under this change, we obtain an explicit expression relating the Cartan connection associated to (M,L) and the transformed Car...

The geometric constructions are performed on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also induced unique forms by a metric tensor (the Levi Civita and the canonical distin...