Abstract
We present a Gauss–Bonnet type formula for complete surfaces in n-dimensional hyperbolic space $$\mathbb{H}^{n}$$ under some assumptions on their asymptotic behaviour. As in recent results for Euclidean submanifolds (see Dillen–Kühnel [4] and Dutertre [5]), the formula involves an ideal defect, i.e., a term involving the geometry of the set of points at infinity.
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