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
Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic t...Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.展开更多
We discuss the twistor quantization problem for the classical system (V d ,A d ), represented by the phase space V d , identified with the Sobolev space H 0 1/2 (S 1,? d ) of half-differentiable vector functions on th...We discuss the twistor quantization problem for the classical system (V d ,A d ), represented by the phase space V d , identified with the Sobolev space H 0 1/2 (S 1,? d ) of half-differentiable vector functions on the circle, and the algebra of observables A d , identified with the semi-direct product of the Heisenberg algebra of V d and the algebra Vect(S 1) of tangent vector fields on the circle.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).
文摘Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.
基金supported by the RFBR(Grant Nos.06-02-04012,08-01-00014)the program of Support of Scientific Schools(Grant No.NSH-3224.2008.1)Scientific Program of RAS"Nonlinear Dynamics"
文摘We discuss the twistor quantization problem for the classical system (V d ,A d ), represented by the phase space V d , identified with the Sobolev space H 0 1/2 (S 1,? d ) of half-differentiable vector functions on the circle, and the algebra of observables A d , identified with the semi-direct product of the Heisenberg algebra of V d and the algebra Vect(S 1) of tangent vector fields on the circle.
