A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors gi...A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors give a complete classifica-tion for regular time-like conformal homogeneous hypersurfaces in R41 with three distinct principal curvatures.展开更多
A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformat...A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformation of R_1~4. Using the projective light-cone model, for those whose shape operators have three distinct real eigenvalues, we calculate the integrability conditions by constructing a scalar conformal invariant and a canonical moving frame in this paper. Similar to the Riemannian case, these hypersurfaces can be determined by the solutions to some system of partial differential equations.展开更多
In this paper, we give a complete conformal classification of the regular space-like hyper- surfaces in the de Sitter Space S~＋1 with parallel para-Blaschke tensors.
Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigi...Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.展开更多
基金supported by the Principal’s Fund(No.KJ2020002)the second is supported by the National Natural Science Foundation of China(Nos.11671330 and 11871405)the third is supported by the National Natural Science Foundation of China(Nos.11831005,1196131001).
文摘A hypersurface x(M)in Lorentzian space R41 is called conformal homogeneous,if for any two points p,q on M,there exists,a conformal transformation of R41,such that(x(M))=x(M),(x(p))=x(q).In this paper,the authors give a complete classifica-tion for regular time-like conformal homogeneous hypersurfaces in R41 with three distinct principal curvatures.
基金supported by National Natural Science Foundation of China (Grant Nos. 11331002, 11471021 and 11601513)the Fundamental Research Funds for Central Universitiesthe Project of Fujian Provincial Department of Education (Grant No. JA15123)
文摘A three dimensional Lorentzian hypersurface x : M_1~3→ R_1~4 is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, and this property is preserved under the conformal transformation of R_1~4. Using the projective light-cone model, for those whose shape operators have three distinct real eigenvalues, we calculate the integrability conditions by constructing a scalar conformal invariant and a canonical moving frame in this paper. Similar to the Riemannian case, these hypersurfaces can be determined by the solutions to some system of partial differential equations.
基金Supported by Foundation of Natural Sciences of China(Grant Nos.11671121,11171091 and 11371018)
文摘In this paper, we give a complete conformal classification of the regular space-like hyper- surfaces in the de Sitter Space S~＋1 with parallel para-Blaschke tensors.
基金supported by the National Natural Science Foundation of China(No.12271069)the Natural Science Foundation of Chongqing(No.cstc2021jcyj-msxm X0443)+1 种基金the Chongqing“Zhitongche”foundation for doctors(No.CSTB2022BSXM-JCX0101)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJQN202201138)。
文摘Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.
