Infinitesimal rigidity and flexibility of a non-symmetric affine connection space
A geometric magnitude (object) \(A\) is called rigid or invariant under the infinitesimal transformation \(\bar x^i=x^i+\varepsilon z^i(x)\) if \(\bar A=A\), and flexible if \(\bar A\neq A\). The authors consider an affine (linear) connection (over a manifold \(M\)) with non-symmetric coefficients, and investigate the rigidity of this connection and its five curvature tensors by means of the Lie derivatives. They give explicit expressions of these Lie derivatives, and they obtain necessary and sufficient conditions for the rigidity.
scientific article; zbMATH DE number 5713508
scientific article