In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex ...In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.展开更多
For all minimal immersions of the 2-sphere S<sup>2</sup> into the unit 2m-sphere S<sup>2m</sup>with area 2π[m（m+1）+2],we are able to give an explicit representation by some real parameters.T...For all minimal immersions of the 2-sphere S<sup>2</sup> into the unit 2m-sphere S<sup>2m</sup>with area 2π[m（m+1）+2],we are able to give an explicit representation by some real parameters.This representation is rather important in the study of minimal 2-spheres in S<sup>2m</sup>because the parameters concerned are independent of each other.Particular examples are given and a classification theorem is also obtained.展开更多
We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space.A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-posi...We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space.A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.展开更多
In this paper we study,using moving frames,conformal minimal two-spheres S2 immersed into a complex hyperquadric Qn equipped with the induced Fubini-Study metric from a complex projective n+1-space CPn+1.Two associate...In this paper we study,using moving frames,conformal minimal two-spheres S2 immersed into a complex hyperquadric Qn equipped with the induced Fubini-Study metric from a complex projective n+1-space CPn+1.Two associated functions τX and τY are introduced to classify the problem into several cases.It is proved that τX or τY must be identically zero if f:S2 → Qn is a conformal minimal immersion.Both the Gaussian curvature K and the Khler angle θ are constant if the conformal immersion is totally geodesic.It is also shown that the conformal minimal immersion is totally geodesic holomorphic or antiholomorphic if K = 4.Excluding the case K = 4,conformal minimal immersion f:S2 → Q2 with Gaussian curvature K2 must be totally geodesic with(K,θ) ∈ {(2,0),(2,π/2),(2,π)}.展开更多
We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional ...We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional Heisenberg group and in the product of the hyperbolic plane with the real line.展开更多
The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C^2 must be equivalent to a trivial vector field by a holomorphic change...The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C^2 must be equivalent to a trivial vector field by a holomorphic change of coordinates. Other classification results are obtained for polynomial vector fields having a finitely curved orbit on C^2.展开更多
基金Project supported by the National Natural Science Foundation of China (10271106)
文摘In terms of the almost complex affine connection and moving unitary frames, all totally rael minimal immersions from R-2 into the nearly Kahler S-6 axe determine explicitly. Moreover, the complete flat almost complex curves in the nearly Kahler S-6 are determined completely.
文摘For all minimal immersions of the 2-sphere S<sup>2</sup> into the unit 2m-sphere S<sup>2m</sup>with area 2π[m（m+1）+2],we are able to give an explicit representation by some real parameters.This representation is rather important in the study of minimal 2-spheres in S<sup>2m</sup>because the parameters concerned are independent of each other.Particular examples are given and a classification theorem is also obtained.
基金This work is partially supported by the National Science Foundation of China
文摘We study the volume growth of the geodesic balls of a minimal submanifold in a Euclidean space.A necessary condition for the isometric minimal immersion into a Euclidean space is obtained. A classification of non-positively curved minimal hypersurfaces in a Euclidean space is given.
基金supported by National Natural Science Foundation of China (Grant No.11071248)Knowledge Innovation Funds of CAS (Grant No.KJCX3-SYW-S03)the President Fund of GUCAS
文摘In this paper we study,using moving frames,conformal minimal two-spheres S2 immersed into a complex hyperquadric Qn equipped with the induced Fubini-Study metric from a complex projective n+1-space CPn+1.Two associated functions τX and τY are introduced to classify the problem into several cases.It is proved that τX or τY must be identically zero if f:S2 → Qn is a conformal minimal immersion.Both the Gaussian curvature K and the Khler angle θ are constant if the conformal immersion is totally geodesic.It is also shown that the conformal minimal immersion is totally geodesic holomorphic or antiholomorphic if K = 4.Excluding the case K = 4,conformal minimal immersion f:S2 → Q2 with Gaussian curvature K2 must be totally geodesic with(K,θ) ∈ {(2,0),(2,π/2),(2,π)}.
基金Work partially supported by RAS,INdAM,FAPESP and CNPq
文摘We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional Heisenberg group and in the product of the hyperbolic plane with the real line.
文摘The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C^2 must be equivalent to a trivial vector field by a holomorphic change of coordinates. Other classification results are obtained for polynomial vector fields having a finitely curved orbit on C^2.
