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Tangent Lie algebras to the holonomy group of a Finsler manifold

Zoltán Muzsnay, Péter T. Nagy (2011)

Communications in Mathematics

Our goal in this paper is to make an attempt to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. First, we introduce the notion of the curvature algebra, generated by curvature vector fields, then we define the infinitesimal holonomy algebra by the smallest Lie algebra of vector fields on an indicatrix, containing the curvature vector fields and their horizontal covariant derivatives with respect to...

The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group.

Dekimpe, K., De Rock, B., Pouseele, H. (2006)

Fixed Point Theory and Applications [electronic only]

The Srní lectures on non-integrable geometries with torsion

Ilka Agricola (2006)

Archivum Mathematicum

This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics—in particular superstring theory—where these naturally appear. Connections with skew-symmetric torsion are exhibited as one of the main tools to understand non-integrable geometries. To this aim a a series of key examples is presented and successively dealt with using the notions of...

The tangent bundle of an almost-complex free loopspace.

Morava, Jack (2003)

Homology, Homotopy and Applications

TQFT's and gerbes.

Picken, Roger (2004)

Algebraic & Geometric Topology

Transitive conformal holonomy groups

Jesse Alt (2012)

Open Mathematics

For (M, [g]) a conformal manifold of signature (p, q) and dimension at least three, the conformal holonomy group Hol(M, [g]) ⊂ O(p + 1, q + 1) is an invariant induced by the canonical Cartan geometry of (M, [g]). We give a description of all possible connected conformal holonomy groups which act transitively on the Möbius sphere S p,q, the homogeneous model space for conformal structures of signature (p, q). The main part of this description is a list of all such groups which also act irreducibly...