We give,in this paper,a monotonicity formula for the Chern-Moser-Weyl curvature tensor under the action of holomorphic embeddings between Levi non-degenerate hypersurfaces with the same positive signature.As an applic...We give,in this paper,a monotonicity formula for the Chern-Moser-Weyl curvature tensor under the action of holomorphic embeddings between Levi non-degenerate hypersurfaces with the same positive signature.As an application,we provide some concrete examples of algebraic Levi non-degenerate hypersurfaces with positive signature that are not embeddable into a hyperquadric of the same signature in a complex space of higher dimension.展开更多
The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of th...The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of the recent studies of Bishop surfaces, which, in particular, includes the work of the authors. In the second part of the paper, we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant. More precisely, we let M be a real submanifold of C 2 defined by an equation of the form w = zz + 2Re(z s + az s+1 ) with s≥ 3 and a a complex parameter. We will prove in the second part of the paper that for s≥ 4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation. When s = 3, we show that surfaces of this type with two different real parameters are not holomorphically equivalent.展开更多
基金supported by National Science Foundation (Grant No. 0801056)
文摘We give,in this paper,a monotonicity formula for the Chern-Moser-Weyl curvature tensor under the action of holomorphic embeddings between Levi non-degenerate hypersurfaces with the same positive signature.As an application,we provide some concrete examples of algebraic Levi non-degenerate hypersurfaces with positive signature that are not embeddable into a hyperquadric of the same signature in a complex space of higher dimension.
基金supported in part by US National Science Foundation (Grant No.0801056)supported in part by National Natural Science Foundation of China (Grant No.10901123)+1 种基金Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090141120010)Ky and Yu-Fen Fan Fund from American Mathematical Society, and a research fund from Wuhan University(Grant No. 1082002)
文摘The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of the recent studies of Bishop surfaces, which, in particular, includes the work of the authors. In the second part of the paper, we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant. More precisely, we let M be a real submanifold of C 2 defined by an equation of the form w = zz + 2Re(z s + az s+1 ) with s≥ 3 and a a complex parameter. We will prove in the second part of the paper that for s≥ 4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation. When s = 3, we show that surfaces of this type with two different real parameters are not holomorphically equivalent.
