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Scalar curvature of a hypersurface

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 https://robertabramsonpl.com

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

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Scalar curvature of a hypersurface

COMPACT HYPERSURFACES WITH CONSTANT …

WebJan 28, 2024 · In particular, the 1st, 2nd and n -th Weingarten curvature correspond to mean curvature, scalar curvature and Gauss curvature respectively. We call a hypersurface … WebSCALAR CURVATURE OF HYPERSURFACES 415 THEOREM 1.4. Let M be an n-dimensional closed hypersurface with constant mean curvature H satisfying H ≤ε(n) in a unit sphere Sn+1,n≤ 7, and S the squared length …

Scalar curvature of a hypersurface

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WebThe scalar curvature is the weakest curvature invariant one can attach (point-wise) to a Riemannian n-manifold Mn. Its value at any point can be described in ... stable minimal hypersurface in M dual to a non-zero class in H1(M;Z), then Nalso admits a metric of positive scalar curvature. WebThe total scalar curvature of Mn is defined to be fM„ \A\" , which is a generalization of the total curvature for surfaces. We call this integral total scalar curvature since for minimal submanifolds of Euclidean space, \A\ is equal to minus one times the scalar curvature.

WebUpload PDF Discover. Log in Sign up. Home 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 …

WebFundamental function in Finsler manifold defines a metrices that depend on a point and a direction. At any point tangent space is a Riemannian and an indicatrix is a convex hypersurface. In this paper a mean curvature … WebIn this study, some identities involving the Riemannian curvature invariants are presented on lightlike hypersurfaces of a statistical manifold in the Lorentzian settings. Several inequalities characterizing lightlike hypersurfaces are obtained. These inequalities are also investigated on lightlike hypersurfaces of Lorentzian statistical space forms.

WebDec 1, 2001 · The paper considers n -dimensional hypersurfaces with constant scalar curvature of a unit sphere Sn−1 (1).

WebDec 8, 1986 · Hypersurfaces with constant scalar curvature Theorem 1. Let Mnbe an n-dimensional compact hyper surf ace embedded in the Euclidean space R/7+1. If the … ef ryethavehttp://www.numdam.org/item/ASNSP_2010_5_9_3_541_0.pdf continuation form uifWebNov 30, 2012 · It is well known to geometric analyst that the scalar curvature of a Riemannian manifold can be decomposed to two parts: one part has a divergence … efr travel companies houseefry dartmouthWebSep 3, 2024 · We derive an upper bound on the waiting time for a non star-shaped hypersurface in $\\mathbb{R}^{n+1}$ moving by Inverse Mean Curvature Flow to become star-shaped. Combining this result with an embeddedness principle for the flow, we provide an upper bound on the maximal time of existence for initial surfaces which are not … continuation forexWebExercise 6. If is a stable minimal hypersurface in ( M;g) which has non-negative Ricci curvature, show that is totally geodesic (i.e., II = 0 along ) and Ric g( ; ) = 0. For the next … efry hamiltonWebDec 29, 2024 · Incompressible hypersurface, positive scalar curvature and positive mass theorem. In this paper, we prove for that if a differentiable -manifold contains a relatively … continuation from previous page