Boundary and lens rigidity for non-convex manifolds

We study the boundary and lens rigidity problems on domains without assuming convexity of boundary. show that such rigidities hold when domain is a simply connected compact Riemannian surface conjugate points. For more general class non-trapping surfaces with no points, we rigidity. also prove injectivity X-ray transform tensors in variety settings non-convex and, some situations, allowing non-empty trapped set.