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Search: All articles in the CMB digital archive with keyword Riemannian manifold

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1. CMB 2010 (vol 53 pp. 674)

Kristály, Alexandru; Papageorgiou, Nikolaos S.; Varga, Csaba
Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
We study a semilinear elliptic problem on a compact Riemannian manifold with boundary, subject to an inhomogeneous Neumann boundary condition. Under various hypotheses on the nonlinear terms, depending on their behaviour in the origin and infinity, we prove multiplicity of solutions by using variational arguments.

Keywords:Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions
Categories:58J05, 35P30

2. CMB 2005 (vol 48 pp. 340)

Andruchow, Esteban
Short Geodesics of Unitaries in the $L^2$ Metric
Let $\M$ be a type II$_1$ von Neumann algebra, $\tau$ a trace in $\M$, and $\l2$ the GNS Hilbert space of $\tau$. We regard the unitary group $U_\M$ as a subset of $\l2$ and characterize the shortest smooth curves joining two fixed unitaries in the $L^2$ metric. As a consequence of this we obtain that $U_\M$, though a complete (metric) topological group, is not an embedded riemannian submanifold of $\l2$

Keywords:unitary group, short geodesics, infinite dimensional riemannian manifolds.
Categories:46L51, 58B10, 58B25

3. CMB 2002 (vol 45 pp. 378)

Fernández-López, Manuel; García-Río, Eduardo; Kupeli, Demir N.
The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry
A partial differential equation, the local M\"obius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local M\"obius equation and an additional partial differential equation.

Keywords:submersion, Möbius equation, twisted product, warped product, product Riemannian manifolds
Categories:53C12, 58J99

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