729 citations
- The University of MelbourneAU30 papers
- Monash UniversityAU25 papers
- Commonwealth Scientific and Industrial Research OrganisationAU22 papers
- The University of QueenslandAU19 papers
- The University of SydneyAU13 papers
- UNSW SydneyAU13 papers
- Australian National UniversityAU12 papers
- Centre National de la Recherche ScientifiqueFR12 papers
- Data61AU12 papers
- Kyushu UniversityJP12 papers
- RMIT UniversityAU10 papers
- Australian SynchrotronAU9 papers
5 papers · 2 filters
The Duality principle for Osserman algebraic curvature tensors
Y. Nikolayevsky, Z. Rakić
We prove that for an algebraic curvature tensor on a pseudo-Euclidean space, the Jordan-Osserman condition implies the Rakić duality principle, and that the Osserman condition and…
Shape maps for second order partial differential equations
O. Rossi, D. J. Saunders, G. E. Prince
We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a cong…
Locally conformally Berwald manifolds and compact quotients of reducible manifolds by homotheties
Vladimir S. Matveev, Yuri Nikolayevsky
We study locally conformally Berwald metrics on closed manifolds which are not globally conformally Berwald. We prove that the characterization of such metrics is equivalent to cha…
Torsion and the second fundamental form for distributions
G. E. Prince
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally…
An intrinsic and exterior form of the Bianchi identities
Thoan Do, Geoff Prince
We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without t…