Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with different...Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.展开更多
Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 k...Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.展开更多
In this paper we give the proof about the equivalence of the complete Einstein- K■hler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of ...In this paper we give the proof about the equivalence of the complete Einstein- K■hler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of two metrics.展开更多
We have derived a set of field equations for a Weyssenhoff spin fluid including magnetic interaction among the spinning particles prevailing in spatially homogeneous, but anisotropically cosmological models of Bianchi...We have derived a set of field equations for a Weyssenhoff spin fluid including magnetic interaction among the spinning particles prevailing in spatially homogeneous, but anisotropically cosmological models of Bianchi type V based on Einstein Cartan theory. We analyze the field equations in three different equations of states specified by p =(1/3)ρ, p =ρ and p =0. The analytical solutions found are non singular provided that the combined energy arising from matter spin and magnetic interaction among particles overcomes the anisotropy energy in the Universe. We have also deduced that the minimum particle numbers for the radiation ( p =(1/3)ρ ) and matter ( p =0) epochs are 10 88 and 10 108 respectively, the minimum particle number for the state p =ρ is 10 96 , leading to the conclusion that we must consider the existence of neutrinos and other creation of particles and anti particles under torsion and strong gravitational field in the early Universe.展开更多
In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly,we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new me...In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly,we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Khler metric on the Cartan-Hartogs domain of the fourth type.展开更多
In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which...In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which intervenes between -2k and -1. This is the sharp estimate.展开更多
Let Y_Ⅳ be the Super-Cartan domain of the fourth type. We reduce the Monge-Ampereequation for the metric to an ordinary differential equation in the auxiliary function X=X(Z, W). Thisdifferential equation can be solv...Let Y_Ⅳ be the Super-Cartan domain of the fourth type. We reduce the Monge-Ampereequation for the metric to an ordinary differential equation in the auxiliary function X=X(Z, W). Thisdifferential equation can be solved to give an implicit function in X. We give the generating functionof the Einstein-Kahler metric on Y_Ⅳ. We obtain the explicit form of the complete Einstein-Kahlermetric on Y_Ⅳ for a special case.展开更多
Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comp...Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.展开更多
Complex Monge-Ampère equation is a nonlinear equation with high degree,so its solution is very diffcult to get.How to get the plurisubharmonic solution of Dirichlet problem of complex Monge- Ampère equation ...Complex Monge-Ampère equation is a nonlinear equation with high degree,so its solution is very diffcult to get.How to get the plurisubharmonic solution of Dirichlet problem of complex Monge- Ampère equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method in this paper.Firstly,the complex Monge-Ampère equation is reduced to a nonlinear secondorder ordinary differential equation(ODE)by using quite different method.Secondly,the solution of the Dirichlet problem is given in semi-explicit formula,and under a special case the exact solution is obtained.These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain.展开更多
文摘Although General Relativity is the classic example of a physical theory based on differential geometry, the momentum tensor is the only part of the field equation that is not derived from or interpreted with differential geometry. This work extends General Relativity and Einstein-Cartan theory by augmenting the Poincaré group with projective (special) conformal transformations, which are translations at conformal infinity. Momentum becomes a part of the differential geometry of spacetime. The Lie algebra of these transformations is represented by vectorfields on an associated Minkowski fiber space. Variation of projective conformal scalar curvature generates a 2-index tensor that serves as linear momentum in the field equations of General Relativity. The computation yields a constructive realization of Mach’s principle: local inertia is determined by local motion relative to mass at conformal infinity in each fiber. The vectorfields have a cellular structure that is similar to that of turbulent fluids.
文摘Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.
文摘In this paper we give the proof about the equivalence of the complete Einstein- K■hler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of two metrics.
文摘We have derived a set of field equations for a Weyssenhoff spin fluid including magnetic interaction among the spinning particles prevailing in spatially homogeneous, but anisotropically cosmological models of Bianchi type V based on Einstein Cartan theory. We analyze the field equations in three different equations of states specified by p =(1/3)ρ, p =ρ and p =0. The analytical solutions found are non singular provided that the combined energy arising from matter spin and magnetic interaction among particles overcomes the anisotropy energy in the Universe. We have also deduced that the minimum particle numbers for the radiation ( p =(1/3)ρ ) and matter ( p =0) epochs are 10 88 and 10 108 respectively, the minimum particle number for the state p =ρ is 10 96 , leading to the conclusion that we must consider the existence of neutrinos and other creation of particles and anti particles under torsion and strong gravitational field in the early Universe.
文摘In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly,we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Khler metric on the Cartan-Hartogs domain of the fourth type.
文摘In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which intervenes between -2k and -1. This is the sharp estimate.
基金Supported by National Natural Science Foundation of China(Grant No.10471097)Scientific Research Common Program of Beijing Municipal Commission of Education(Grant NO.KM200410028002)Supported by National Natural Science Foundation of China(Grant No
文摘Let Y_Ⅳ be the Super-Cartan domain of the fourth type. We reduce the Monge-Ampereequation for the metric to an ordinary differential equation in the auxiliary function X=X(Z, W). Thisdifferential equation can be solved to give an implicit function in X. We give the generating functionof the Einstein-Kahler metric on Y_Ⅳ. We obtain the explicit form of the complete Einstein-Kahlermetric on Y_Ⅳ for a special case.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10071051 and 10171068)Natural Science Foundation of Beijing(Grant Nos.1002004 and 1012004).
文摘Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.
基金supported by the Research Foundation of Beijing Government(Grant No.YB20081002802)National Natural Science Foundation of China(Grant No.10771144)
文摘Complex Monge-Ampère equation is a nonlinear equation with high degree,so its solution is very diffcult to get.How to get the plurisubharmonic solution of Dirichlet problem of complex Monge- Ampère equation on the Cartan-Hartogs domain of the second type is discussed by using the analytic method in this paper.Firstly,the complex Monge-Ampère equation is reduced to a nonlinear secondorder ordinary differential equation(ODE)by using quite different method.Secondly,the solution of the Dirichlet problem is given in semi-explicit formula,and under a special case the exact solution is obtained.These results may be helpful for the numerical method of Dirichlet problem of complex Monge-Ampère equation on the Cartan-Hartogs domain.
