A contribution of the generalized Bochner technique to the geometry of complete minimal submanifolds

S. E. Stepanov^ab, I. I. Tsyganok<sup>b

a</sup> All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences, Moscow
^b Financial University under the Government of the Russian Federation, Moscow

Abstract: In this paper, based on methods of the Bochner technique, which is an important part of the geometric analysis, we establish conditions under which minimal and stable minimal submanifolds in Riemannian manifolds are characterized as totally geodesic submanifolds.

Keywords: Euclidean space, Riemannian manifold, minimal hypersurface, stable hypersurface, rigidity theorem

UDC: 514.7

MSC: 53C20, 53C21, 53C24

DOI: 10.36535/2782-4438-2024-236-22-30