On the analytic and geometric aspects of obstruction flatness
作者机构：Department of Mathematics University of California at San Diego School of Mathematics (Zhuhai) Sun Yat-sen University
出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报(英文版))
年 卷 期：2024年
核心收录：
基 金：supported in part by the NSF grant DMS-1900955 and DMS-2154368 supported in part by the NSF grants DMS-1800549 and DMS-2045104 supported in part by the NSFC grant No. 12201040
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 ? Cncan 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.
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