State representation is used to discuss the link with two variables， and the estimation of breadth of the two variables(say I and m) is given for S-links.
We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel secon...We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.展开更多
We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.
This paper considers the existence problem of an elliptic equation, which is equivalent to the prescribing conformal Gaussian curvature problem on R^2. An existence result is proved. In particular, K（x） is allowed t...This paper considers the existence problem of an elliptic equation, which is equivalent to the prescribing conformal Gaussian curvature problem on R^2. An existence result is proved. In particular, K（x） is allowed to be unbounded above.展开更多
A new framework for free-form surface design is proposed. Using manifolds can generalize the spline scheme to surfaces of arbitrary topology. Physics-based modeling incorporate physical laws into shape representation ...A new framework for free-form surface design is proposed. Using manifolds can generalize the spline scheme to surfaces of arbitrary topology. Physics-based modeling incorporate physical laws into shape representation to provide direct shape interaction. The combination presents a new method inherits the attractive properties of the manifold surface as well as that of the physics-based models.展开更多
In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz ...In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S1(m+1) in L1(m+2) and is of 1-type in L1(m+2).展开更多
in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1...in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.展开更多
文摘State representation is used to discuss the link with two variables， and the estimation of breadth of the two variables(say I and m) is given for S-links.
文摘We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.
文摘We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
基金Supported by the NSF of Education Department of Henan Province(20021100002)Supported by the NSF of Education Department of Henan Province(200510475038)
文摘Let M be a concircularly fiat totally real minimal submanifold in CP4. The infimum Vm of the volume V （M） of M is obtained, also the necessary and sufficient conditions of ＂V（M）=Vm＂ is given.
文摘This paper considers the existence problem of an elliptic equation, which is equivalent to the prescribing conformal Gaussian curvature problem on R^2. An existence result is proved. In particular, K（x） is allowed to be unbounded above.
基金Funded by the Chinese National Natural Science Foundation (No.50105013).
文摘A new framework for free-form surface design is proposed. Using manifolds can generalize the spline scheme to surfaces of arbitrary topology. Physics-based modeling incorporate physical laws into shape representation to provide direct shape interaction. The combination presents a new method inherits the attractive properties of the manifold surface as well as that of the physics-based models.
基金Supported by the Education Commission of Henan Province(20021100002) Supported by the NSF of Henan University(200110475028)
文摘In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S1(m+1) in L1(m+2) and is of 1-type in L1(m+2).
文摘in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.
