Hipersuperfícies de curvaturas média e escalar constantes

Abstract

In this work we will perform a detailed study on the compact hypersurfaces of constant and average curvatures immersed in the Sn + 1 sphere. In chapter 2 we will introduce the basic prerequisites, which will support the main results. In chapter 3 we find the lemmas that will serve the conclusions of the theorems mentioned in the introduction. In sequence, we will first have some necessary identities. In Chapter 4, we consider a compact surface of M elevated from a sphere with a constant mean curvature H. By the definition of tensor fi, we show that if square magnitude is greater than or equal to Bh, where Bh is different from 0 is a number that depends only on H and n, then modulus of square is congruent to 0 or modulus of square is congruent to Bh. We also characterize all high M n with square congruent module congruent to Bh. In Chapter 5, the objective is to demonstrate Theorems (1.4) and (1.5).