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
We propose a new framework for image-based three-dimensional(3D) model retrieval. We first model the query image as a Euclidean point. Then we model all projected views of a 3D model as a symmetric positive definite(S...We propose a new framework for image-based three-dimensional(3D) model retrieval. We first model the query image as a Euclidean point. Then we model all projected views of a 3D model as a symmetric positive definite(SPD) matrix, which is a point on a Riemannian manifold. Thus, the image-based 3D model retrieval is reduced to a problem of Euclid-to-Riemann metric learning. To solve this heterogeneous matching problem, we map the Euclidean space and SPD Riemannian manifold to the same high-dimensional Hilbert space, thus shrinking the great gap between them. Finally, we design an optimization algorithm to learn a metric in this Hilbert space using a kernel trick. Any new image descriptors, such as the features from deep learning, can be easily embedded in our framework. Experimental results show the advantages of our approach over the state-of-the-art methods for image-based 3D model retrieval.展开更多
By introducing an imaginary space transform curvature ρx, a complex space called Riemannian space is constructed, in which the light propagating in free space has the trajectory of straight line while propagating. Mo...By introducing an imaginary space transform curvature ρx, a complex space called Riemannian space is constructed, in which the light propagating in free space has the trajectory of straight line while propagating. Moreover, this curvature couples with that of the wave front of the paraxial beam ρw, and therefore a complex curvatureρe is constructed, which can be employed to investigate the behavior of the light transmission and to generalize the ABCD law.展开更多
Some of the variation formulas of a metric were derived in the literatures by using the local coordinates system, In this paper, We give the first and the second variation formulas of the Riemannian curvature tensor, ...Some of the variation formulas of a metric were derived in the literatures by using the local coordinates system, In this paper, We give the first and the second variation formulas of the Riemannian curvature tensor, Ricci curvature tensor and scalar curvature of a metric by using the moving frame method. We establish a relation between the variation of the volume of a metric and that of a submanifold. We find that the latter is a consequence of the former. Finally we give an application of these formulas to the variations of heat invariants. We prove that a conformally flat metric g is a critical point of the third heat invariant functional for a compact 4-dimensional manifold M, then （M, g） is either scalar flat or a space form.展开更多
The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fed...The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.展开更多
The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The ...The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.展开更多
In this paper, we have considered a class curves with some geometric properties in a higher dimensional space and obtained the differential equation of such a class curves, which are called the hyperbolas. We have con...In this paper, we have considered a class curves with some geometric properties in a higher dimensional space and obtained the differential equation of such a class curves, which are called the hyperbolas. We have considered also hyperbola-preserving conformal transformation and the relevant physical sense. And therefore obtained other invariant properties under the illustrious concircular transformation.展开更多
We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
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
由于脑电信号具有低信噪比、非平稳等特点,传统脑机接口需对用户执行长时间的校准训练,才能建立可靠、准确的分类模型。针对当前迁移学习在脑电信号上分类准确率低的问题,本研究提出了基于黎曼空间特征迁移学习(Riemannian space featur...由于脑电信号具有低信噪比、非平稳等特点,传统脑机接口需对用户执行长时间的校准训练,才能建立可靠、准确的分类模型。针对当前迁移学习在脑电信号上分类准确率低的问题,本研究提出了基于黎曼空间特征迁移学习(Riemannian space feature transfer learning,RFTL)的运动想象脑电信号分类算法。该算法首先在黎曼空间对源域和目标域数据进行分布对齐后,利用联合分布适配减少不同域间的数据分布差异,构建适用于目标域任务的域不变分类器模型。实验结果表明,RFTL算法可有效解决跨域分布的不一致性,显著提高运动想象脑电信号跨对象的识别准确率,改善脑机接口研究中的通用性问题。展开更多
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).
基金supported by the National Key R&D Program of China(No.2017YFB1002600)the National Natural Science Foundation of China(No.61272304)+1 种基金the Natural Science Foundation of Zhejiang Province,China(Nos.LQ16F020007 and LQ17F030002)the Natural Science Foundation of Ningbo,China(No.2017A610108)
文摘We propose a new framework for image-based three-dimensional(3D) model retrieval. We first model the query image as a Euclidean point. Then we model all projected views of a 3D model as a symmetric positive definite(SPD) matrix, which is a point on a Riemannian manifold. Thus, the image-based 3D model retrieval is reduced to a problem of Euclid-to-Riemann metric learning. To solve this heterogeneous matching problem, we map the Euclidean space and SPD Riemannian manifold to the same high-dimensional Hilbert space, thus shrinking the great gap between them. Finally, we design an optimization algorithm to learn a metric in this Hilbert space using a kernel trick. Any new image descriptors, such as the features from deep learning, can be easily embedded in our framework. Experimental results show the advantages of our approach over the state-of-the-art methods for image-based 3D model retrieval.
基金Project supported by the National Hi-Tech Inertial Confinement Fusion Committee,the Guangdong Natural Science Foundation,the Postdoctoral Foundation of Guangdong and National Postdoctoral Foundation of China.
文摘By introducing an imaginary space transform curvature ρx, a complex space called Riemannian space is constructed, in which the light propagating in free space has the trajectory of straight line while propagating. Moreover, this curvature couples with that of the wave front of the paraxial beam ρw, and therefore a complex curvatureρe is constructed, which can be employed to investigate the behavior of the light transmission and to generalize the ABCD law.
基金Supported by National Natural Science Foundation of China (Grant No. 10571088)
文摘Some of the variation formulas of a metric were derived in the literatures by using the local coordinates system, In this paper, We give the first and the second variation formulas of the Riemannian curvature tensor, Ricci curvature tensor and scalar curvature of a metric by using the moving frame method. We establish a relation between the variation of the volume of a metric and that of a submanifold. We find that the latter is a consequence of the former. Finally we give an application of these formulas to the variations of heat invariants. We prove that a conformally flat metric g is a critical point of the third heat invariant functional for a compact 4-dimensional manifold M, then （M, g） is either scalar flat or a space form.
文摘The space of internal geometry of a model of a real crystal is supposed to be finite, closed, and with a constant Gaussian curvature equal to unity, permitting the realization of lattice systems in accordance with Fedorov groups of transformations. For visualizing computations, the interpretation of geometrical objects on a Clifford surface (SK) in Riemannian geometry with the help of a 2D torus in a Euclidean space is used. The F-algorithm ensures a computation of 2D sections of models of point systems arranged perpendicularly to the symmetry axes l3, l4, and l6. The results of modeling can be used for calculations of geometrical sizes of crystal structures, nanostructures, parameters of the cluster organization of oxides, as well as for the development of practical applications connected with improving the structural characteristics of crystalline materials.
基金Supported by the National Natural Science Foundation of China(No.10601066)the financial support of the Fundamental Research Funds for Central Universitiesthe Research Funds of Renmin University of China(11XNI008)
文摘The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.
基金Project supported in part by the National Natural Science Foundation of China (Grant No. 19631060)Beijing Normal University and the State Education Commission of China.
文摘Under certain curvature condition, the existence of spectral gap is proved on path spaces with infinite time-interval.
基金Foundation item: Supported by the Natural Science foundation of Henan Education Committee (20021100002)
文摘In this paper, we have considered a class curves with some geometric properties in a higher dimensional space and obtained the differential equation of such a class curves, which are called the hyperbolas. We have considered also hyperbola-preserving conformal transformation and the relevant physical sense. And therefore obtained other invariant properties under the illustrious concircular transformation.
文摘We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space.We carried out the divergence of a vector field on it and obtained a formula of Simons’type.
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.
文摘由于脑电信号具有低信噪比、非平稳等特点,传统脑机接口需对用户执行长时间的校准训练,才能建立可靠、准确的分类模型。针对当前迁移学习在脑电信号上分类准确率低的问题,本研究提出了基于黎曼空间特征迁移学习(Riemannian space feature transfer learning,RFTL)的运动想象脑电信号分类算法。该算法首先在黎曼空间对源域和目标域数据进行分布对齐后,利用联合分布适配减少不同域间的数据分布差异,构建适用于目标域任务的域不变分类器模型。实验结果表明,RFTL算法可有效解决跨域分布的不一致性,显著提高运动想象脑电信号跨对象的识别准确率,改善脑机接口研究中的通用性问题。
