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Simplicial nonpositive curvature

Tadeusz Januszkiewicz, Jacek Świątkowski (2006)

Publications Mathématiques de l'IHÉS

We introduce a family of conditions on a simplicial complex that we call local k-largeness (k≥6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the non-positive curvature: locally 6-large spaces have many properties similar to non-positively curved ones. However, local 6-largeness neither implies nor is implied by non-positive curvature of the standard metric. One can think of these results as a higher...

Simultaneous unitarizability of SL n ℂ -valued maps, and constant mean curvature k-noid monodromy

Wayne Rossman, Nicholas Schmitt (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into SL n ℂ under conjugation by a single analytic matrix map.We apply this result to the monodromy arising from an integrable partial differential equation to construct a family of k -noids, genus-zero constant mean curvature surfaces with three or more ends in euclidean, spherical and hyperbolic 3 -spaces.

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

Zdeněk Dušek (2015)

Czechoslovak Mathematical Journal

Let ( M , g ) be a 4-dimensional Einstein Riemannian manifold. At each point p of M , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p . In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O ( 4 ) acts as a transformation group between ST bases at T p M and for the so-called 2-stein curvature tensors, the group Sp ( 1 ) ⊂ SO ( 4 ) acts as a transformation group...

Singular BGG sequences for the even orthogonal case

Lukáš Krump, Vladimír Souček (2006)

Archivum Mathematicum

Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.

Singular Poisson reduction of cotangent bundles.

Simon Hochgerner, Armin Rainer (2006)

Revista Matemática Complutense

We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.

Singular Poisson-Kähler geometry of certain adjoint quotients

Johannes Huebschmann (2007)

Banach Center Publications

The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group SL(n,ℂ), we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.

Currently displaying 121 – 140 of 864