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ISOMETRY GROUPS OF RIEMANNIAN MANIFOLDS WITH BOUNDED NORMS
Mathematical Institute, Tohoku University 2006 Tohoku mathematical journal Vol.58 No.2
<P>We generalize several results on the order of the isometry group of a compact manifold with negative Ricci curvature proved by Dai et al. under the assumption of bounded norm and an integral curvature bound. We also show that there exists a bound on the order of the isometry group depending on the weak norm of $M$.</P>
Gilkey, Peter V.,Kim, Chan Yong,Park, JeongHyeong MATHEMATICAL INSTITUTE OF TOHOKU UNIVERSITY 2017 Tohoku mathematical journal Vol.69 No.1
<P>We use the solution space of a pair of ODEs of at least second order to construct a smooth surface in Euclidean space. We describe when this surface is a proper embedding which is geodesically complete with finite total Gauss curvature. If the associated roots of the ODEs are real and distinct, we give a universal upper bound for the total Gauss curvature of the surface which depends only on the orders of the ODEs and we show that the total Gauss curvature of the surface vanishes if the ODEs are second order. We examine when the surfaces are asymptotically minimal.</P>
Schrodinger uncertainty relation and convexity for the monotone pair skew information
Ko, C.K.,Yoo, H.J. MATHEMATICAL INSTITUTE OF TOHOKU UNIVERSITY 2014 Tohoku mathematical journal Vol.66 No.1
Furuichi and Yanagi showed a Schrodinger uncertainty relation for the Wigner-Yanase-Dyson skew information, which is a special monotone pair skew information. In this paper, we give a Schrodinger uncertainty relation based on a monotone pair skew information, and extend the result of Furuichi and Yanagi. Moreover, we show that some monotone pair skew information becomes a metric adjusted skew information and therefore the convexity of it follows from known results.
A note on Rhodes and Gottlieb-Rhodes groups
Choi, Kyoung Hwan,Jo, Jang Hyun,Moon, Jae Min MATHEMATICAL INSTITUTE OF TOHOKU UNIVERSITY 2016 Tohoku mathematical journal Vol.68 No.1
<P>The purpose of this paper is to give positive answers to some questions which are related to Fox, Rhodes, Gottlieb-Fox, and Gottlieb-Rhodes groups. Firstly, we show that for a compactly generated Hausdorff based G-space (X, x(0), G) with free and properly discontinuous G-action, if (X, x(0), G) is homotopically n-equivariant, then the n-th Gottlieb-Rhodes group G sigma(n) (X, x(0), G) is isomorphic to the n-th Gottlieb-Fox group G tau(n) (X/G, p(x(0))). Secondly, we prove that every short exact sequence of groups is n-Rhodes-Fox realizable for any positive integer n. Finally, we present some positive answers to restricted realization problems for Gottlieb-Fox groups and Gottlieb-Rhodes groups.</P>