The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.展开更多
The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like subm...The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.展开更多
For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-d...For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-dual spinor bundle on M.Now V(D)forms an almost complex structure on dual bundle.Moreover,they showed that this almost complex structure is integrable if and only if M is self-dual.In this paper,we extend the construction of V(D)to 4-dimensional pseudo-Riemannian manifolds of signature(2,2).And we give a new method to prove the curvature condition in the integrability condition of V(D).Using this new method,we study the integrability conditions and structure of V(D)when the signature of g is(2,2).展开更多
基金Supported by the National Fundations of Natural sciences. Supported by the Henan Fundations of Scientific Committee.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.
文摘The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.
基金Supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(No.YSBR-001)。
文摘For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-dual spinor bundle on M.Now V(D)forms an almost complex structure on dual bundle.Moreover,they showed that this almost complex structure is integrable if and only if M is self-dual.In this paper,we extend the construction of V(D)to 4-dimensional pseudo-Riemannian manifolds of signature(2,2).And we give a new method to prove the curvature condition in the integrability condition of V(D).Using this new method,we study the integrability conditions and structure of V(D)when the signature of g is(2,2).
