The geometric Cauchy problem for the hyperbolic Hessian one equation Martínez López, Antonio Milán López, Francisco Cauchy problem Hyperbolic Hessian one equation Improper affine spheres We solve the problem of finding all indefinite improper affine spheres passing through a given regular curve of R3R3 with a prescribed affine co-normal vector field along this curve. We prove the problem is well-posed when the initial data are non-characteristic and show that uniqueness of the solution can fail at characteristic directions. As application we classify the indefinite improper affine spheres admitting a geodesic planar curve. 2015-09-30T11:31:12Z 2015-09-30T11:31:12Z 2015 info:eu-repo/semantics/article Martínez-López, A.; Milán López, F. The geometric Cauchy problem for the hyperbolic Hessian one equation. Nonlinear Analysis: Theory, Methods and Applications, 125: 323–333 (2015). [http://hdl.handle.net/10481/37917] 0362-546X http://hdl.handle.net/10481/37917 10.1016/j.na.2015.05.021 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License