Notes on Conformal Metrics of Negative Curvature on Manifolds with Boundary (Journal of Mathematical Study, 2024)
We use certain Morse functions to construct conformal metrics such that theeigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, weprove that any Riemannian metric on compact 3-manifolds with boundary is conformal to a compact metric of negative sectional curvature.
Keywords: Schouten tensor; Modified Schouten tensor; conformal deformation; Morse theory.