Catherine Searle

Positively curved manifolds with maximal symmetry-rank

Abstract Grove, K. and Searle, ,Positively curved manifolds with maximal symmetry-rank, Journal of Pure and Applied Algebra 91 (1994) 137–142. The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.

Orientation and Symmetries of Alexandrov Spaces with Applications in Positive Curvature

We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.

The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank

We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold admits an isometric action of a compact Lie group G with principal isotropy group H and cohomogeneity k such that k - (rankG - rank H) l.

Global G-Manifold Reductions and Resolutions

The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.

How to lift positive Ricci curvature

Remark Various definitions of lower Ricci curvature bounds on metric spaces are proposed in Kuwae and Shioya [23], Lott and Villani [25], Ohta [28], Sturm [40; 41] and Zhang and Zhu [50]. Our proof only requires that the quotient space of the principal orbits, M reg=G , has Ricci curvature greater than or equal to 1, and since M reg=G is a Riemannian manifold, it does not matter which definition we choose.

Initial structure of cetyltrimethylammonium bromide micelles in aqueous solution from molecular dynamics simulations

A series of molecular dynamics simulations were performed in order to explore the initial (10.5 ns) structure of CTAB micelles formed in aqueous solutions. The determination of the aggregation number of CTAB is a long-standing and fundamental problem. Therefore we simulated eight model systems of micelles in aqueous solution. Some micellar structural characteristics, local solvation environments, and counter ion distributions are described. Topological and geometrical concepts are used to characterize the resulting micelle structures. Our findings indicate that for certain aggregation numbers micelles are formed by layered spherical structures.

An introduction to spherical orbit spaces

Consider a compact, connected Lie group G acting isometrically on a sphere Sn of radius 1. Two-dimensional quotient spaces of the type Sn/G have been investigated extensively. This paper provides an elementary introduction, for nonspecialists, to this important field by way of several classical examples and supplies an explicit list of all the isotropy subgroups involved in these examples.