法丛平坦子流形的余维数限定
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摘要
研究了空间形式中具有平坦法丛的子流形,通过对其法标架场作变换并结合子流形的结构方程,得到其余维数不超过子流形的维数.
A submanifold with normal bundle flatness in a space form was studied.By transforming the normal frame field and combining with its structural equation,its codimension which is not more than the dimension of the submanifold was obtained.
A submanifold with normal bundle flatness in a space form was studied.By transforming the normal frame field and combining with its structural equation,its codimension which is not more than the dimension of the submanifold was obtained.
引文
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[2] CHEN B Y.Chapter 3 Riemannian submanifolds[J].Handbook of Differential Geometry,2000,1:187-418.
[3] WHITNEY H.Differentiable manifolds[J].Annals of Mathematics,1936,37(3):645-680.
[4] CHERN S S,KUIPER N H.Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space[J].Annals of Mathematics (Second Series),1952,56(3):422-430.
[5] O'NEILL B.Immersion of manifolds of nonpositive curvature[J].Proceedings of the American Mathematical Society,1960,11(1):132-134.
[6] 乐进,吴传喜.关于法丛平坦子流形的余维数减少定理[J].湖北大学学报:自然科学版,1991,13(1):32-37.
[7] ERBACHER J.Reduction of the codimension of an isometric immersion[J].J Differential Geometry,1971,5(3-4),333-340.
[2] CHEN B Y.Chapter 3 Riemannian submanifolds[J].Handbook of Differential Geometry,2000,1:187-418.
[3] WHITNEY H.Differentiable manifolds[J].Annals of Mathematics,1936,37(3):645-680.
[4] CHERN S S,KUIPER N H.Some theorems on the isometric imbedding of compact Riemann manifolds in Euclidean space[J].Annals of Mathematics (Second Series),1952,56(3):422-430.
[5] O'NEILL B.Immersion of manifolds of nonpositive curvature[J].Proceedings of the American Mathematical Society,1960,11(1):132-134.
[6] 乐进,吴传喜.关于法丛平坦子流形的余维数减少定理[J].湖北大学学报:自然科学版,1991,13(1):32-37.
[7] ERBACHER J.Reduction of the codimension of an isometric immersion[J].J Differential Geometry,1971,5(3-4),333-340.