# Correction to: Intrinsic curvature of curves and surfaces and a Gauss–Bonnet theorem in the Heisenberg group

## 1 Correction to: Math. Z. (2017) 287:1–38 https://doi.org/10.1007/s00209-016-1815-6

In the publication [1] there is an unfortunate computational error, which however does not affect the correctness of the main results.

However, noticing that \(\omega (\ddot{\gamma })= \frac{d}{dt}\omega (\dot{\gamma })\) we see that the assertion \(\omega (\ddot{\gamma })(t_0)=0\) is still true for horizontal points that arise as accumulation points of other horizontal points. Since the parameterizing interval is compact, there are at most a finite number of isolated horizontal points \(t_1,\ldots , t_N\) at which the quantity \(\omega (\ddot{\gamma })(t_i)\) may be nonzero, and hence all of the preceding formulas hold at all points of [*a*, *b*] except for this finite number of isolated points.

The main result of the paper, Theorem 1.1, is not affected by these corrections since its proof is based on an approximation argument relying on the Lebesgue dominated convergence theorem. In the application of this theorem a set of countably many points can be ignored as a null set, and the proof works as indicated in Section 6 of the paper.

## Notes

### Acknowledgements

We are grateful to Derek Jung and Maxim Tryamkin for pointing out the error in the proof of Lemma 3.4.

## References

- 1.Balogh, Z.M., Tyson, J.T., Vecchi, E.: Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group. Math. Z.
**287**, 1–38 (2017)MathSciNetCrossRefzbMATHGoogle Scholar