浸入超曲面的度理论
微分几何
2016-10-11 v3
摘要
我们为紧致可定向黎曼流形中具有指定曲率的紧致浸入超曲面发展了一个度理论，其中是任意椭圆曲率函数。我们将该理论应用于计数各种情形下浸入超球面的（代数）个数：其中为平均曲率、外曲率和特殊拉格朗日曲率，并证明在所有情形下，该个数等于，其中是的欧拉示性数。
引用
@article{arxiv.1010.1879,
title = {Degree Theory of Immersed Hypersurfaces},
author = {Harold Rosenberg and Graham Smith},
journal= {arXiv preprint arXiv:1010.1879},
year = {2016}
}
备注
Complete revision. We've worked hard to make the text clearer and we hope the reader will notice the difference. Shorter and more conceptual proofs. The applications, we hope, are much clearer. In addition, we develop a new concept of "weakly smooth manifolds". This provides a nice smooth manifold structure for the space of unparametrised immersions (details in the introduction)