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A theorem on polynomial lorentz structures

Published online by Cambridge University Press:  18 May 2009

Krzysztof Deszyński
Affiliation:
Jagellonian University, Institute of Mathematics, 00-059 KrakóW, Ul Reymonta 4, Poland
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Let M be a differentiable manifold of dimension m. A tensor field f of type (1, 1) on M is called a polynomial structure on M if it satisfies the equation:

where a1, a2, …, an are real numbers and I denotes the identity tensor of type (1, 1).

We shall suppose that for any xM

is the minimal polynomial of the endomorphism fx: TxMTxM.

We shall call the triple (M, f, g) a polynomial Lorentz structure if f is a polynomial structure on M, g is a symmetric and nondegenerate tensor field of type (0, 2) of signature

such that g (fX, fY) = g(X, Y) for any vector fields X, Y tangent to M. The tensor field g is a (generalized) Lorentz metric.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

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