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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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本文研究具强负曲率Cartan-Hadamard流形M~n(n≥3)上给定数量曲率函数S的共形形变问题.利用上下解方法,并通过精心构造上解,我们获得了当完备的共形形变度量存在时,函数S在无穷远附近的最佳渐近性态.在较一般情况下,我们还给出了共形数量曲率方程解的渐近估计. 相似文献