Index of minimal hypersurfaces in real projective spaces

Abstract

We prove that for an embedded unstable one-sided minimal hypersurface of the $(n+1)$-dimensional real projective space, the Morse index is at least $n+2$, and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson surfaces.

Final version, 19 pages

References in corpus (2)

• The index and nullity of the Lawson surfaces ${\xi }_{g,1}$
• The Lawson surfaces are determined by their symmetries and topology