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geodesic flow, connecting orbits and almost full foliation

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Science China Mathematics 2006年第12期49卷 1830-1838页

作者： CHENG Jian MENG Long Department of Mathematics Nanjing UniversityNanjing 210093China Department of MathematicsNanjing UniversityNanjing 210093China

We study in this article a special dynamical behavior of geodesic flow on *** example shows that there is an area-preserving monotone twist map for which all minimal periodic orbits can be connected,and at the same ti... 详细信息

关键词： geodesic flows,rotation numbers,minimal configurations,connecting orbits.

Light rays and waves on geodesic lenses

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Photonics Research 2019年第11期7卷 1266-1272页

作者： Lin Xu Xiangyang Wang Tomas Tyc Chong Sheng Shining Zhu Hui Liu HUANYANG CHEN Institute of Electromagnetics and Acoustics and Key Laboratory of Electromagnetic Wave Science and Detection Technology Xiamen UniversityXiamen 361005China Institutes of Physical Science and Information Technology&Key Laboratory of Opto-Electronic Information Acquisition and Manipulation of Ministry of Education Anhui UniversityHefei 230601China National Laboratory of Solid State Microstructures and School of Physics Collaborative Innovation Center of Advanced MicrostructuresNanjing UniversityNanjing 210093China Department of Theoretical Physics and Astrophysics Masaryk UniversityKotlarska 261137 BrnoCzech Republic

Starting from well-known absolute instruments that provide perfect imaging, we analyze a class of rotationally symmetric compact closed manifolds, namely, geodesic lenses. We demonstrate with a numerical method that light rays confined on geodesic lenses form closed trajectories, and that for optical waves, the spectrum of a geodesic lens is(at least approximately) degenerate and equidistant. Moreover, we fabricate two geodesic lenses in micrometer and millimeter scales and observe curved light rays along the geodesics. Our experimental setup may offer a new platform to investigate light propagation on curved surfaces.

关键词： geodesic curved absolute

Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability

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Science China Mathematics 2000年第12期43卷 1279-1293页

作者：靳全勤 Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of SciencesBeijing 100080 China Department of Mathematics Hebei UniversityBaoding 071002China

In this paper, we determine a large class of totally geodesic submanifolds of a compact Riemannian symmetric *** stability of these submanifolds in their ambient space is also determined.

关键词： compact Riemannian symmetric spaces totally geodesic submanifolds involutive automorphisms of a Lie group (or a Lie algebra) stability.

CONNECTIONS AND geodesic CHARACTERISTIC OF EQUATIONSOF MOTION FOR CONSTRAINED MECHANICAL SYSTEMS

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Applied Mathematics and Mechanics(English Edition) 1998年第9期19卷 837-842页

作者：罗绍凯郭永新梅凤翔 Shangqiu Teachers College Shangqiu P. R. China Department of Applied Mechanics Peking Institute of Technology Beijing P. R. China

The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from the case in an autonomous mechanical system.

关键词： 1-jet bundle dynamical flow vertical endomorphism connection geodesic

Sampling Streaming Data Along geodesic

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Chinese Journal of Electronics 2015年第2期24卷 251-257页

作者： LI Wenping YANG Jing ZHANG Jianpei College of Computer Science and Technology Harbin Engineering University College of Mathematics Physics and Information Engineering Jiaxing University

This paper proposes an approach to sample data stream based on differential geometry. Our aim is to take advantage of information of discarded data and support stream to generate different number of transactions during different periods. To this end, we establish a novel data stream model represented by a surface, within which time is quantified and probability, value and time,viewed as one united body, could be calculated simultaneously. We pro ject data stream onto a surface of the model and replace points which have the shortest geodesic distance with their mid-point. To the best of our knowledge,this is the first work on introducing differential geometry as a sampling trick. Experimental results show that our approach is effective.

关键词： Data stream Sampling Data stream model Differential geometry geodesic

Affine Planar geodesic Immersions with Maximal Codimension

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Acta Mathematica Sinica,English Series 2010年第2期26卷 345-352页

作者： Pawel WITOWICZ Rzeszow Universitu of Technology

This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal. Vrancken classified parallel affine immersions in this case and obtained, among others, generalized Veronese submanifolds. In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case. A geometric interpretation of parallel immersions is also given： The affine immersions with pointwise planar normal sections （with respect to the equiaffine transversal bundle） are parallel. This result is verified for surfaces in R4 and for immersions with the maximal codimension.

关键词： affine immersion geodesic transversal bundle normal section

Totally geodesic submanifolds of maximal rank in symmetric spaces

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Science China Mathematics 2004年第2期47卷 264-271页

作者： ZHU Fuhai & LIANG KeSchool of Mathematical Sciences and LMAM, Peking University, Beijing 100871, China College of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China School of Mathematical Sciences and LMAM Peking University Beijing China College of Mathematical Sciences and LPMC Nankai University Tianjin China

We gave a complete list of totally geodesic submanifolds of maximal rank in symmetric spaces of noncompact type. The compact cases can be obtained by the duality.

关键词： totally geodesic submanifold, Lie triple system, maximal rank.

The Motion of a Gyroscope Freely Falling Along the Radial geodesic in the Space-Time of a Black Hole with a Global Monopole

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Chinese Physics Letters 1993年第7期10卷 445-448页

作者： JING Jiliang YU Hongwei WANG Yongjiu Institute of Physics Hunan Normal UniversityChangsha 410081

By means of the orthonormal frame,the motion of the axis of a gyroscope freely falling along the radial geodesic in the space-time of a black hole with a global monopole is *** is shown that the axis of the gyroscope ... 详细信息

关键词： radial rotate geodesic

geodesic Lightlike Submanifolds of Indefinite Sasakian Manifolds

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Advances in Pure Mathematics 2011年第6期1卷 378-383页

作者： Junhong Dong Ximin Liu 不详

In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, m... 详细信息

关键词： CR-Lightlike Submanifolds Sasakian Manifolds Totally geodesic Submanifolds