双层的Brylinski函数

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-11-21 DOI:10.1016/j.difgeo.2023.102078

Pooja Rani , M.K. Vemuri

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引用次数: 0

摘要

对于d维欧几里德空间上的紧支撑(Schwartz)分布T，定义了Brylinski结函数的类比。这是一个右半平面上的全纯函数。如果T是紧致光滑超表面上的(一致)双层，则函数作为亚纯函数在复平面上有解析延拓，其残数是第二基本形式的不变量的积分。当d=2和d=3时计算前几个残数。

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The Brylinski beta function of a double layer

An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution T on d-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If T is a (uniform) double-layer on a compact smooth hypersurface, then the beta function has an analytic continuation to the complex plane as a meromorphic function, and the residues are integrals of invariants of the second fundamental form. The first few residues are computed when $d = 2$ and $d = 3$ .

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.