For the Obata-type equation with Robin boundary constant c>1 and suitable curvature bounds, the manifold is forced to be a geodesic ball in hyperbolic space, or a warped product over a standard sphere.
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Some rigidity results related to the Obata type equation
For the Obata-type equation with Robin boundary constant c>1 and suitable curvature bounds, the manifold is forced to be a geodesic ball in hyperbolic space, or a warped product over a standard sphere.