Mathematische Zeitschrift Quantization of curvature for compact surfaces in S
نویسندگان
چکیده
Abstract. For minimal surfaces in spheres, there is a well known conjecture about the quantization of intrinsic curvature which has been solved only in special cases so far. We recall an intrinsic and an extrinsic version for the known results and extend them to compact non-minimal surfaces in spheres. In particular we discuss special classes like Willmore surfaces and surfaces with parallel mean curvature vector.
منابع مشابه
Mathematische Zeitschrift A local Steiner–type formula for general closed sets and applications
We introduce support (curvature) measures of an arbitrary closed set A in R and establish a local Steiner–type formula for the localized parallel volume of A. We derive some of the basic properties of these support measures and explore how they are related to the curvature measures available in the literature. Then we use the support measures in analysing contact distributions of stationary ran...
متن کاملMathematische Zeitschrift Extrinsic Killing spinors
Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of nonnegative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a...
متن کاملMathematische Zeitschrift On Einstein four-manifolds with S1-actions
We study closed Einstein 4-manifolds which admit S1 actions of a certain type, i.e., warped products. In particular, we classify them up to isometry when the fixed point of the S1 action satisfies certain natural geometric conditions. The proof uses the Bochner-Weitzenböck formula for 1-forms and the theory of minimal surfaces in 3-manifolds.
متن کاملSpacelike Mean Curvature One Surfaces in De Sitter 3-space
The first author studied spacelike constant mean curvature one (CMC-1) surfaces in de Sitter 3-space S 1 when the surfaces have no singularities except within some compact subset and are of finite total curvature on the complement of this compact subset. However, there are many CMC-1 surfaces whose singular sets are not compact. In fact, such examples have already appeared in the construction o...
متن کاملHyperbolic surfaces of $L_1$-2-type
In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.
متن کامل