| 关于拟常曲率流形的平行中曲本子流形的一个积分不等式 |
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| 引用本文： | 吴金文,汪富泉.关于拟常曲率流形的平行中曲本子流形的一个积分不等式[J].吉首大学学报(自然科学版),1992(1). |
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| 作者姓名： | 吴金文 汪富泉 |
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| 作者单位： | 吉首大学
(吴金文)，四川师院(汪富泉) |
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| 摘 要： | 本文的目的是证明如下的定理:设V~(n+p)是拟常曲率黎曼流形,即V的黎曼曲率张量可表为K_(ABCD)+a(g_(AC)g_(BD)-g_(AD)g_(BC))+b(g_(AC)V_BV_D+g_(BD)V_AV_C-g_(AD)V_(BC)-g_(BC)V_AV_D)(sum from n=(A,B)(g_(AB)V_AV_B=1),若M~n是V~(n+p)的具有平行平均曲率的紧,致无边子流形,则integral from n=M~n({(2-1/p)S~2-na+(1/2)(b-|b|)(n+1)]S+n(n-1)b~2+nH(anH+S~(3/2)+2|b|S~(1/2))}*1≥0)式中S=const是M~n的第二基本形式的长度之平方,H=const是M~n的中曲率.当M~n是V~(n+p)的极小子流形时(H=0),得到白正国教授1]中的相应不等式
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| 关 键 词： | 拟常曲率流形 平行中曲率子流形 积分不等式 |
An integral inequality about parallel meancurvature submainifolds in a Riemannianmanifold with quasi constant curvature |
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| Wu Jinwen Wang Fuquqn.An integral inequality about parallel meancurvature submainifolds in a Riemannianmanifold with quasi constant curvature[J].Journal of Jishou University(Natural Science Edition),1992(1). |
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| Authors: | Wu Jinwen Wang Fuquqn |
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| Abstract: | In this paper , we have established the following result , Theorem Let Vn+p be an n+p-dimensional Riemannian manifold with quasi constant curvature, that is Riemannian
curvature tensor of Vn+p. KABCD = a (gACgBD - gADgBC) + b (gAC VBVD + gBD VBVC-gBC VAVD)
(Where a and b are arbitrary functions on Vn+p,VAis a arbitrary unit vector field, and (?)
VAVB=1), If Mn is a compact submanifold with parallel mean curvature in a Riemannian manifold with quasi constant curvature , then
Where S1/2 is the length of the second fundamental form of Mn. When Mn is a minimal submanifold of Vn+p, we have obtained that integral inequality in1]. |
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| Keywords: | quasi-constant curvature manifold parallel mean curvature submanifold integral inequality |
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