Our purpose is to study the minimal tori in the hyperquadric Q2.Firstly,we obtain a necessary and sufcient condition for the minimal surface in Qnwhich is also minimal in CPn+1.Next,we show that this kind of minimal s...Our purpose is to study the minimal tori in the hyperquadric Q2.Firstly,we obtain a necessary and sufcient condition for the minimal surface in Qnwhich is also minimal in CPn+1.Next,we show that this kind of minimal surface(neither holomorphic nor anti-holomorphic) with constant curvature in Q2 is part of a flat totally real torus.Finally,we prove that totally real minimal flat tori in Q2 must be totally geodesic,and we classify all the totally geodesic closed surfaces in Q2.展开更多
We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost compl...We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost complex curves,we obtain some interesting global results with respect to Gaussian curvature,area and the genus.展开更多
We study the area-minimization property of the cones over Stiefel manifolds V_(m)(F^(n))(F=R,C or H)and their products,where the Stiefel manifolds are embedded into the unit sphere of Euclidean space in a standard way...We study the area-minimization property of the cones over Stiefel manifolds V_(m)(F^(n))(F=R,C or H)and their products,where the Stiefel manifolds are embedded into the unit sphere of Euclidean space in a standard way.We will show that these cones are areaminimizing if the dimension is at least 7,using the Curvature Criterion of[Mem.Amer.Math.Soc.,1991,91(446):vi+111 pp.].This extends the results of corresponding references,where the cones over products of Grassmann manifolds were considered.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11071248 and 11226079)Program of Natural Science Research of Jiangsu Higher Education Institutions of China(Grant No.12KJD110004)
文摘Our purpose is to study the minimal tori in the hyperquadric Q2.Firstly,we obtain a necessary and sufcient condition for the minimal surface in Qnwhich is also minimal in CPn+1.Next,we show that this kind of minimal surface(neither holomorphic nor anti-holomorphic) with constant curvature in Q2 is part of a flat totally real torus.Finally,we prove that totally real minimal flat tori in Q2 must be totally geodesic,and we classify all the totally geodesic closed surfaces in Q2.
基金supported by National Natural Science Foundation of China(Grant No.11071248)
文摘We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost complex curves,we obtain some interesting global results with respect to Gaussian curvature,area and the genus.
基金Supported by NSFC(No.11871450)Project of Stable Support for Youth Team in Basic Research Field,CAS(No.YSBR-001).
文摘We study the area-minimization property of the cones over Stiefel manifolds V_(m)(F^(n))(F=R,C or H)and their products,where the Stiefel manifolds are embedded into the unit sphere of Euclidean space in a standard way.We will show that these cones are areaminimizing if the dimension is at least 7,using the Curvature Criterion of[Mem.Amer.Math.Soc.,1991,91(446):vi+111 pp.].This extends the results of corresponding references,where the cones over products of Grassmann manifolds were considered.
