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  

An integral inequality about parallel meancurvature submainifolds in a Riemannianmanifold with quasi constant curvature

作　　者：吴金文[1] 汪富泉[2] 

机构地区：[1]吉首大学 [2]四川师院

出　　处：《吉首大学学报》1992年第5期12-17,共6页

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)。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 in[1].

关 键 词：拟常曲率流形 平行中曲率 子流形 

分 类 号：O189.31[理学—数学]