C^3中Legendre曲线的Calabi-Yau问题及其应用
微分几何
2012-05-24 v2
摘要
我们在C^3中构造了一个完备、有界的Legendre浸入。作为其直接应用，我们展示了双曲3-空间中弱完备有界平坦front、de Sitter 3-空间中弱完备有界平坦front以及R^3中弱完备有界非正常仿射front的首批例子。
引用
@article{arxiv.1107.0106,
title = {Calabi-Yau Problem for Legendrian curves in C^3 and applications},
author = {Francisco Martin and Masaaki Umehara and Kotaro Yamada},
journal= {arXiv preprint arXiv:1107.0106},
year = {2012}
}
备注
After the submission, the authors found that the proof of the main theorem contains a serious error and the main theorem turns to be an open problem. ArXiv:1205.4779 is a new paper showing the existence of a weakly complete flat surface (with singularities) in hyperbolic 3-space such that the images of the hyperbolic Gauss maps are bounded, which plays a role of a recovery of the present paper