Remark on the curvature of equilateral hyperbola [PDF]
, 1909 Josef Kounovský
openalex +1 more source
Rigidity of noncompact complete manifolds with harmonic curvature [PDF]
arXiv, 2009 Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n \ge 5$ and $L_{n/2}$ norms of Weyl curvature and traceless Ricci curvature are small enough.
arxiv
Scalar curvature, isoperimetric collapse and General Relativity in the Constant Mean Curvature gauge [PDF]
arXiv, 2010 We discuss a set of relations, set in the form of results, conjectures and problems, between the L^{2}-norm of the Ricci curvature of a 3-manifold, the scalar curvature and the volume radius. We illustrate the scope of these relations with potential applications to the Einstein Constant Mean Curvature flow (or GR seen as a geometric flow of constant ...
arxiv
Surfaces in E3 invariant under a one parameter group of isometries of E3
Anais da Academia Brasileira de Ciências, 2000 We develop a convenient surface theory in E³ in order to apply it to the class of the surfaces invariant under a one-parameter group of isometries of E³.
ROUSSOS IOANNIS M.
doaj
A remark to the curvature and to the problem of normals of central conics [PDF]
, 1914 Josef Kounovský
openalex +1 more source
Minimal hypersurfaces in $\mathbb{S}^5$ with constant scalar curvature and zero Gauss curvature are totally geodesic [PDF]
arXivWe show that a closed minimal hypersurface in $\mathbb{S}^5$ with constant scalar curvature and zero Gauss curvature is totally geodesic.
arxiv
On the extension of axially symmetric volume flow and mean curvature flow [PDF]
arXiv, 2013 We study the provenance of singularity formation under mean curvature flow and volume preserving mean curvature flow in an axially symmetric setting. We prove that if the mean curvature is uniformly bounded on any finite time interval, then no singularities can develop during that time under both mean curvature flow and volume preserving mean curvature
arxiv
Nomogram for the radius of curvature of Archimedean spiral [PDF]
, 1935 Alexander Fischer
openalex +1 more source
Comparison geometry of manifolds with boundary under a lower weighted Ricci curvature bound [PDF]
arXiv, 2016 We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition, and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric ...
arxiv