Scholarlink

<p>In this paper, we investigate analytic and geometric properties of obstruction flatness of strongly pseudoconvex CR hypersurfaces of dimension 2<i>n</i> − 1. Our first two results concern local aspects. One asserts that any strongly pseudoconvex CR hypersurface <i>M</i> ⊂ ℂ<sup><i>n</i></sup> can be osculated at a given point <i>p</i> ∈ <i>M</i> by an obstruction flat one up to order 2<i>n</i> + 4 generally and 2<i>n</i> + 5 if and only if <i>p</i> is an obstruction flat point. In the other result, we show that locally there are non-spherical but obstruction flat CR hypersurfaces with <i>transverse symmetry</i> for <i>n</i> = 2. The final main result in this paper concerns the existence of obstruction flat points on compact, strongly pseudoconvex, 3-dimensional CR hypersurfaces. It asserts that the unit sphere in a negative line bundle over a Riemann surface <i>X</i> always has at least one circle of obstruction flat points.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the Analytic and Geometric Aspects of Obstruction Flatness

  • 期刊论文

  • 发表日期：

    2025年9月10日

查看全文
  • Peter Ebenfelt,
  • Ming Xiao,
  • Hang Xu

摘要

In this paper, we investigate analytic and geometric properties of obstruction flatness of strongly pseudoconvex CR hypersurfaces of dimension 2n − 1. Our first two results concern local aspects. One asserts that any strongly pseudoconvex CR hypersurface M ⊂ ℂn can be osculated at a given point p ∈ M by an obstruction flat one up to order 2n + 4 generally and 2n + 5 if and only if p is an obstruction flat point. In the other result, we show that locally there are non-spherical but obstruction flat CR hypersurfaces with transverse symmetry for n = 2. The final main result in this paper concerns the existence of obstruction flat points on compact, strongly pseudoconvex, 3-dimensional CR hypersurfaces. It asserts that the unit sphere in a negative line bundle over a Riemann surface X always has at least one circle of obstruction flat points.