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Invariant torsion and G2-metrics

Diego Conti, Thomas Bruun Madsen (2015)

Complex Manifolds

We introduce and study a notion of invariant intrinsic torsion geometrywhich appears, for instance, in connection with the Bryant-Salamon metric on the spinor bundle over S3. This space is foliated by sixdimensional hypersurfaces, each of which carries a particular type of SO(3)-structure; the intrinsic torsion is invariant under SO(3). The last condition is sufficient to imply local homogeneity of such geometries, and this allows us to give a classification. We close the circle by showing that...

Invariant vector fields of Hamiltonians

Jacek Dębecki (1998)

Archivum Mathematicum

A complete classification of natural transformations of Hamiltonians into vector fields on symplectic manifolds is given herein.

Invariants and flow geometry

J. González-Dávila, L. Vanhecke (1999)

Colloquium Mathematicae

We continue the study of Riemannian manifolds (M,g) equipped with an isometric flow ℱ ξ generated by a unit Killing vector field ξ. We derive some new results for normal and contact flows and use invariants with respect to the group of ξ-preserving isometries to charaterize special (M,g, ℱ ξ ), in particular Einstein, η-Einstein, η-parallel and locally Killing-transversally symmetric spaces. Furthermore, we introduce curvature homogeneous flows and flow model spaces and derive an algebraic characterization...

Invariants homotopiques attachés aux fibrés symplectiques

Pierre Dazord (1979)

Annales de l'institut Fourier

On donne une construction géométrique d’invariants généralisant la classe de Maslov-Arnold d’une immersion lagrangienne dans un fibré cotangent et l’indice de Maslov-Arnold-Leray d’une immersion lagrangienne 2 q -orientée dans R n ⊕ R n * : la classe de Maslov-Arnold universelle d’un fibré symplectique et l’indice de Maslov-Arnold-Leray d’un fibré q -symplectique, c’est-à-dire dont le groupe structural est le revêtement à q feuillets de S p ( n ) . Tout ceci relève d’une situation géométrique générale dans laquelle s’introduisent...

Invariants of complex structures on nilmanifolds

Edwin Alejandro Rodríguez Valencia (2015)

Archivum Mathematicum

Let ( N , J ) be a simply connected 2 n -dimensional nilpotent Lie group endowed with an invariant complex structure. We define a left invariant Riemannian metric on N compatible with J to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [7], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving...

Invertible Carnot Groups

David M. Freeman (2014)

Analysis and Geometry in Metric Spaces

We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.

Isometric Embeddings of Pro-Euclidean Spaces

Barry Minemyer (2015)

Analysis and Geometry in Metric Spaces

In [12] Petrunin proves that a compact metric space X admits an intrinsic isometry into En if and only if X is a pro-Euclidean space of rank at most n, meaning that X can be written as a “nice” inverse limit of polyhedra. He also shows that either case implies that X has covering dimension at most n. The purpose of this paper is to extend these results to include both embeddings and spaces which are proper instead of compact. The main result of this paper is that any pro-Euclidean space of rank...

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