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Associated with an immersion φ : S~3→■, we can define a canonical bundle endomorphism F : TS~3→ TS~3 by the pull back of the K?hler form of ■. In this article,related to F we study equivariant minimal immersions from S~3 into ■ under the additional condition(?_XF)X = 0 for all X ∈ ker(F). As main result, we give a complete classification of such kinds of immersions. Moreover, we also construct a typical example of equivariant non-minimal immersion φ : S~3→■ satisfying(?_XF)X = 0 for all X ∈ ker(F), which is neither Lagrangian nor of CR type. 相似文献
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In this paper,it is proved that the Sasakian anti-holomorphic submanifolds of a Kaehlerian manifold is characterized by D-totally umbilical,and some curvature properties of the CR-submanifolds are ohtained. 相似文献
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本文研究预定高斯曲率时H~2(-1)上共形高斯曲率方程的可解性和不可解性,给出H~2(-1)上旋转对称函数是其上共形高斯曲率的一个充分条件,特别地证明了:H~2(-1)上每个非负的旋转对称函数都是其上无穷多个共形度量的高斯曲率 相似文献
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常曲率空间中具平行平均曲率向量的子流形 总被引:6,自引:0,他引:6
本文利用第二基本形式的长度平方和平均曲率的关系研究常曲率空间中具平行平均曲率向量的子流形为全脐的pinching问题,获得了一定条件下的最佳pinching区间,并确定了phincning区间端点处对应非全脐子流形的分类. 相似文献
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Hypersurfaces with Constant Mean Curvature in Space FormsHypersurfaceswithConstantMeanCurvatureinSpaceForms¥SongHongzao;HuZej... 相似文献
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In this paper,it is proved that the Sasakian anti-holomorphic submanifolds of a Kaehlerian man-ifold is characterized by D-totally umbilical,and some curvature properties of the CR-submanifolds are ob-tained. 相似文献
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胡泽军 《数学物理学报(A辑)》2000,20(4):474-479
设(M^m,g)是一个n维的完备黎曼流形,其Ricci曲率满足RicM(x)≥-A(1 r^2(x)ln^2(2 r(x))),其中A是非负常数,r(x)表示点x∈M到某固定点x0∈M的测地距离。则M上方程△u Su Ku^a=0在下述条件“⑴在M上S≤0;⑵在M上K<0且有常数a>0使在一个紧集之外K≤-a^2;⑶常数a>1”下的C^2-非负解只有零解。 相似文献