The Geodesic X-ray Transform with a $$GL(n,\mathbb {C})$$-Connection
The Geodesic X-ray Transform with a $$GL(n,\mathbb {C})$$-Connection
Abstract We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of all such transforms in a neighborhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the …