In this paper, we investigate the relaxation phenomenon for quasilinear hyperbolic conservation laws, and obtain global smooth solutions and the life span of classical solutions to its Cauchy problem. These results sh...In this paper, we investigate the relaxation phenomenon for quasilinear hyperbolic conservation laws, and obtain global smooth solutions and the life span of classical solutions to its Cauchy problem. These results shows that the relaxation admits the effects of dissipation.展开更多
In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvatu...In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.展开更多
We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in...We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds.展开更多
Based on a general variational principle, Einstein–Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a resul...Based on a general variational principle, Einstein–Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a result of mistaking different geometrical, physical ob jects as one and the same. It is also pointed out that in a curved spacetime, the sum vector of matter energy-momentum over a finite hyper-surface can not be defined. In curvilinear coordinate systems conservation of matter energy-momentum is not the continuity equations for its components. Conservation of matter energy-momentum is the vanishing of the covariant divergence of its density-flux tensor field. Introducing gravitational energy-momentum to save the law of conservation of energy-momentum is unnecessary and improper. After reasonably defining "change of a particle's energy-momentum", we show that gravitational field does not exchange energy-momentum with particles. And it does not exchange energy-momentum with matter fields either. Therefore, the gravitational field does not carry energy-momentum, it is not a force field and gravity is not a natural force.展开更多
基金Supported by the NSF of China(t0571024)Supported by the NSF of Henan Province(200511051700)Supported by the NSF of Educational Department of Henan Province(200510078005)
文摘In this paper, we investigate the relaxation phenomenon for quasilinear hyperbolic conservation laws, and obtain global smooth solutions and the life span of classical solutions to its Cauchy problem. These results shows that the relaxation admits the effects of dissipation.
文摘In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.
基金supported by Science Foundation of Guangdong Province (Grant No. S2012010010038)National Natural Science Foundation of China (Grant No. 11571215)supporting project from the Department of Education of Guangdong Province (Grant No. Yq2013073)
文摘We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds.
文摘Based on a general variational principle, Einstein–Hilbert action and sound facts from geometry, it is shown that the long existing pseudotensor, non-localizability problem of gravitational energy-momentum is a result of mistaking different geometrical, physical ob jects as one and the same. It is also pointed out that in a curved spacetime, the sum vector of matter energy-momentum over a finite hyper-surface can not be defined. In curvilinear coordinate systems conservation of matter energy-momentum is not the continuity equations for its components. Conservation of matter energy-momentum is the vanishing of the covariant divergence of its density-flux tensor field. Introducing gravitational energy-momentum to save the law of conservation of energy-momentum is unnecessary and improper. After reasonably defining "change of a particle's energy-momentum", we show that gravitational field does not exchange energy-momentum with particles. And it does not exchange energy-momentum with matter fields either. Therefore, the gravitational field does not carry energy-momentum, it is not a force field and gravity is not a natural force.
