论文标题
关于阻塞平坦的分析和几何方面
On the analytic and geometric aspects of obstruction flatness
论文作者
论文摘要
在本文中，我们研究了尺寸$ 2N-1 $的强质量CR CR超曲面的阻塞平坦度的分析和几何特性。我们的前两个结果涉及当地方面。定理3.2断言，任何强烈的pseudoconvex cr hypersurface $ m \ subset \ subset \ mathbb {c}^n $都可以在给定点$ p \ in m $的给定点$ p \ in m $上进行示意，最多是$ 2N+4 $ $ 4 $ $ 4 $，并且只有$ 2n+$ 2n+5 $，并且只有$ 2n+5 $，并且只有$ p $ p $是flastion Flankion Flat Points flastion Flat Points flastion Flat Point。在定理4.1中，我们在本地表明，有横向对称性的非球形但阻塞扁平的CR超曲面，其横向对称性为$ n = 2 $。本文的最终主要结果涉及紧凑，强烈的伪有线，三维CR Hypersurfaces的障碍物平坦点。定理5.1断言，在黎曼表面$ x $上的负线束中的单位球总是至少有一个障碍物平坦点。
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. Theorem 3.2 asserts that any strongly pseudoconvex CR hypersurface $M\subset \mathbb{C}^n$ can be osculated at a given point $p\in M$ 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 Theorem 4.1, 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. Theorem 5.1 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.
