具有余维数为 1 的全测地叶状的欧几里得超曲面
微分几何
2014-01-27 v2
摘要
我们对携带具有完备叶且余维数为 1 的全测地叶状的欧几里得空间超曲面进行了分类。特别地，我们证明了具有完备剖面的余维数为 1 的旋转超曲面由其在 warped product 结构所刻画。此外，还考虑了该问题的局部版本。
引用
@article{arxiv.1306.4570,
title = {Euclidean hypersurfaces with a totally geodesic foliation of codimension one},
author = {M. Dajczer and V. Rovenski and R. Tojeiro},
journal= {arXiv preprint arXiv:1306.4570},
year = {2014}
}
备注
15 pages. Final version. To appear in Geometriae Dedicatta. Theorem 6 in the previous version removed, details on some of the proofs added, overall exposition improved