The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space
The lightlike flat geometry on spacelike submanifolds of codimension two in Minkowski space
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DOI：
10.1007/s00029-007-0033-9
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发表时间：
2006-04
期刊：
影响因子：
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通讯作者：
S. Izumiya;M. C. R. Romero Fuster
中科院分区：
文献类型：
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作者：
S. Izumiya;M. C. R. Romero Fuster
在Minkowski空间中，对余维为2的类空子流形引入了光锥Gauss-Kronecker曲率的概念，它是欧氏空间中超曲面的Gauss曲率的一般概念的推广.在局部意义上，这个曲率描述了这样的子流形与类光超平面的接触。我们研究了这种曲率的几何性质，并证明了Gauss-Bonnet型定理。例如，我们有双曲空间中的超曲面、光锥中的类空超曲面和德西特空间中的类空超曲面。
We introduce the notion of the lightcone Gauss–Kronecker curvature for a spacelike submanifold of codimension two in Minkowski space, which is a generalization of the ordinary notion of Gauss curvature of hypersurfaces in Euclidean space. In the local sense, this curvature describes the contact of such submanifolds with lightlike hyperplanes. We study geometric properties of such curvatures and show a Gauss–Bonnet type theorem. As examples we have hypersurfaces in hyperbolic space, spacelike hypersurfaces in the lightcone and spacelike hypersurfaces in de Sitter space.