An index upper bound for non-orientable minimal surfaces in the $n-$dimensional Euclidean space

Vladimir Medvedev

Published 2022-04-17Version 1

In the present paper we obtain an upper bound on the Morse index of a complete (possibly branched) immersed non-orientable minimal surface in the $n-$dimensional Euclidean space. It is an analog of the upper bound of Ejiri and Micallef for orientable surfaces. The obtained upper bound enables us to compute the index of the Alarc\'on-Forstneri\v{c}-L\'opez M\"obius band in the 4-dimensional Euclidean space. According to our computation it is equal to one. In Appendix we discuss inequalities on the index of a closed non-orientable minimal surface in a general Riemannian manifold.