The Anomaly Formula of the Analytic Torsion on CR Manifolds with S^1 action

Abstract

Let X be a compact connected strongly pseudoconvex CR manifold of dimension 2n+1, n ≥ 1 with a transversal CR S 1 -action on X. In this paper we introduce the Quillen metric on the determinant line of the Fourier components of the Kohn-Rossi cohomology on X with respect to the S 1 -action. We study the behavior of the Quillen metric under the change of the metrics on the manifold X and on the vector bundle over X. We obtain an anomaly formula for the Quillen metric on X with respect to the S 1 -action.

The Bochner-Kodaira-Nakano formula for line bundles on CR manifolds with transversal CR R-action

“…The Bochner-Kodaira-Nakano formula [2] plays an important role in complex geometry, which is related to some classical results like Kodaira embedding theorem and Riemann-Roch-Hirzebruch formula. The counterpart of these results are well established for CR manifold with transversal CR S 1 -action [4,1] and related recent progress [11] [12] [14] [10] [6]. However, the Bochner-Kodaira-Nakano formula seems absent in this context.…”

Pseudo-relatives and restrictive-relatives in child Mandarin

“…We think that there may be something peculiar about Chinese shi…de clefts that contributes to the object-gap dominance found in pseudo-RCs in our study. That is, an object NP is not allowed to be positioned to the right of SHI as a focused constituent (Teng, 1979; Huang, 1988; Tsao, 1994). In English, an object NP is allowed to be moved into It is … that configuration to have an object-focus reading as in (24a).…”

“…In English, an object NP is allowed to be moved into It is … that configuration to have an object-focus reading as in (24a). However, in Mandarin, due to some special syntactic restrictions, an object cleft in a shi…de construction like (24b) is unacceptable (Huang, 1988; Tsao, 1994; Yang & Ku 2010). The best way to represent the object-focus reading of the English cleft in (24a) is to use a pseudo-cleft construction like (24c), which actually involves an object-gap, like Example (17) in our data.…”

Writing of Business Ethnography: Reflections on Fieldwork and Theory

“…On the other hand, practice logic based on a local culture has been emphasized. The differences existing in local knowledge has resulted in different adjustment and development paths of the economy, market and knowledge structure of local communities (Huang 2012). Both the structure of local markets and the system of world economy have become increasingly complex rather than homogeneous (Berger 2002).…”