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Some modified connection structures associated with the Finslerian gravitational field. (English) Zbl 1106.53018

Summary: Some modified connection structures of the Finslerian gravitational field are considered by modifying the Finslerian independent variables \((x^i,y^i)\) \((i,j=1,2,3,4)\) in the following forms: \((x^i,y^i,p_j)\) \((p_j\): co-vector dual to \(y^i\)); \((x^i,y^i,z^k)\) (\(z^k\): another vector chosen at one more microscopic level than the \(y\)-level); \((x,\psi)\) (\(\psi\): spinor).

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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