Webin a scalar-flat hypersurface, similar to the flux formula for a regular end in a minimal surface. In Section 3 we prove the theorem on two-ended scalar-flat hypersurfaces. We present in an appendix (Section 4) the asymptotic expansion, at infinity, of a rotational scalar-flat graph. The notion of a regular scalar-flat end relies on that ... WebMany examples of biconservative hypersurfaces have constant mean curvature. A famous conjecture of Bang-Yen Chen on Euclidean spaces says that everybiharmonic submanifold has null mean curvature. Inspired by Chen conjecture, we study biconservative Lorentz submanifolds of the Minkowski spaces.
On compact minimal hypersurfaces in a sphere with constant scalar curvature
WebA closed hypersurface M n of constant scalar curvature R and constant mean curvature H in S n+ι is isoparametric provided it has 3 distinct principal curvatures everywhere. REMARK. When the principal curvatures are all non-simple, R. Miyaoka [7] exhibited that M n is isoparametric even without assuming the scalar curvature is constant. WebJul 9, 2024 · A piece of a minimally immersed hypersurface of constant scalar curvature in S 4 is isoparametric. For the case n = 4, T. Lusala, M. Scherfner and L. Sousa Jr. [11] … continuation form
Abstract. arXiv:2304.05208v1 [math.DG] 11 Apr 2024
Webon a new geometric argument which relates the scalar curvature and mean curvature of a hypersurface to the mean curvature of the level sets of a height function. By extending the … Webspacelike hypersurface of a Lorentzian manifold (Sn;1;g~) with pbeing the second fundamental form. The components T 00 and T ... the scalar curvature and the mean curvature of the boundary are strictly positive. Then the boundary @M and a plane asymptotically parallel to @M serve as the WebIn this paper, we study conformally flat hypersurfaces of dimension in using the framework of Möbius geometry. First, we classify and explicitly express the conformally flat hypersurfaces of dimension with constant … continuation form jrf