In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group ther...In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.展开更多
The differential geometry of curves on a hypersphere in the Euclidean space reflects instantaneous properties of spherecal motion. In this work, we give some results for differential geometry of spacelike curves in 3-...The differential geometry of curves on a hypersphere in the Euclidean space reflects instantaneous properties of spherecal motion. In this work, we give some results for differential geometry of spacelike curves in 3-dimensional de-Sitter space. Also, we study the Frenet reference frame, the Frenet equations, and the geodesic curvature and torsion functions to analyze and characterize the shape of the curves in 3-dimensional de-Sitter space.展开更多
We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-...We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-th mean curvature （r=1,2,…,n-1）.When r=1 we recover Montiel’s result.展开更多
基金The project partially supported by National Natural Science Foundation of China under Grant No. 10231050/A010109
文摘In 1935 Dirac established the physical wave equations in the de-Sitter spaces but neither energy-momentum operators nor their conservative laws were given. In this article it is proved that in the de-Sitter group there is a subgroup group isomorphic to the Heisenberg group and the generators of this groups are the energy-momentum operators which obey a conservative law.
文摘The differential geometry of curves on a hypersphere in the Euclidean space reflects instantaneous properties of spherecal motion. In this work, we give some results for differential geometry of spacelike curves in 3-dimensional de-Sitter space. Also, we study the Frenet reference frame, the Frenet equations, and the geodesic curvature and torsion functions to analyze and characterize the shape of the curves in 3-dimensional de-Sitter space.
基金Li Haizhong is supported by NNSFC No.19701017 Basic Science Research Foundation of Tsinghua University Chen Weihua is supported by NNSFC No.19571005
文摘We establish integral formulas of Minkowski’s type for compact spacelike hypersurfaces in de sitter space S<sub>1</sub><sup>n+1</sup>（1）and give their applications to the case of constant r-th mean curvature （r=1,2,…,n-1）.When r=1 we recover Montiel’s result.
