2023/09/28 by Dajczer, Marcos, Jimenez, Miguel Ibieta
#53A07 #53B25 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2309.16086
Classifying the nonflat hypersurfaces in Euclidean space f\colon Mn→ℝn+1 that locally admit smooth infinitesimal deformations that preserve the Gauss map infinitesimally was a problem only considered by Schouten \citeSc in 1928. He found two conditions that are necessary and sufficient, with the first one being the minimality of the submanifold. The second is a technical condition that does not clarify much about the geometric nature of the hypersurface. In that respect, the parametric solution of the problem given in this note yields that the submanifold has to be Kaehler.