Harmonic and isometric rotations around a curve (Q1320940)

The paper studies local rotations around a smooth embedded curve in a Riemannian manifold \(M\). Such rotations are defined by means of a given family of rotations around the tangent to the curve in its normal bundle, and the exponential mapping. The authors derive, in the analytic case, a set of necessary and sufficient conditions for the rotations to be isometries of \(M\). They also investigate the relationship between isometric rotations and harmonic rotations. In particular, both notions are shown to coincide when \(M\) is a locally symmetric Einstein space and the curve is a geodesic.