The Classification Of Closed Minimal Hypersurfaces With Constant Non-negative Scalar Curvature In S~7(1)

In this dissertation, we consider Chern’s conjecture about 6- dimensional case. Let M6 â†' S7 be a 6-dimensional closed minimally immersed hypersurface of S7 with constant non-negative scalar curvature. M. Scherfner · L. Vrancken · S. Weiss (2012) [16] had proved that the conclusion with the conditions of H=f3=fs= 0, f4= constant and the scalar curvature R≥ 0. As the principle curvature of M6 had been subject to too many restriction with the conditions thatf3=f5= 0, we replacef3=f5= 0 withf3= constant andf5= constant. Inspired by Bing Tang, Ling Yang (2015) [21] and S. P. Chang (1993)[5], we make that the number of the principal curvature g is constant to prove the conclusion according the different value of g and to get the classification of M6.