Topic
Riemann curvature tensor
About: Riemann curvature tensor is a research topic. Over the lifetime, 6248 publications have been published within this topic receiving 138871 citations. The topic is also known as: Riemann–Christoffel tensor.
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TL;DR: In this article, the authors describe the geometry and topology of a compact simply connected positively curved Riemannian 6-manifold F′ which is related to the flag manifold F over C P2, and an infinite series of simply connected circle bundles over F′ with positive sectional curvature.
Abstract: We describe the geometry and the topology of a compact simply connected positively curved Riemannian 6-manifold F′ which is related to the flag manifold F over C P2, and an infinite series of simply connected circle bundles over F′, also with positive sectional curvature. All of these spaces are biquotients of the Lie group SU (3) and they are not homeomorphic to a homogeneous space of positive curvature.
80 citations
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TL;DR: This paper studies the convergence of general threshold dynamics type approx- imation schemes to hypersurfaces moving with normal velocity depending on the normal direction and the curvature tensor to study the mean curvature evolution.
Abstract: We study the convergence of general threshold dynamics type approx- imation schemes to hypersurfaces moving with normal velocity depending on the normal direction and the curvature tensor. We also present results about the asymptotic shape of fronts propagating by threshold dynamics. Our results generalize and extend models introduced in the theories of cellular automaton and motion by mean curvature. In this paper we study the convergence of general threshold dynamics type ap- proximation schemes to hypersurfaces moving with normal velocity depending on the normal direction and the curvature tensor. These schemes are generalizations and extensions of the threshold dynamics models introduced by Gravner and Grieath (GrGr) to study cellular automaton modeling of excitable media and by Bence, Merriman and Osher (BMO) to study the mean curvature evolution. Cellular automaton models are mathematical models used to understand the transmission of periodic waves through environments such as a network or a tissue. A common feature of many such models is that some threshold level of excitation must occur in a neighborhood of a location to become excited and conduct a pulse. Typical physical systems which exhibit such phenomenology are, among others, neural networks, cardiac muscle, Belousov-Zhabotinsky oscillating chemical reaction, etc. Interfaces (fronts, hypersurfaces) in R N evolving with normal velocity V ¼ vðDn;nÞ; ð0:1Þ
80 citations
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80 citations