Metric Connections in Projective Differential Geometry
By Michael Eastwood, V. Matveev. 2008
110 citations recorded by the source corpus.
We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sections of a certain vector bundle with connection. This vector bundle and its connection are derived from the Cartan connection of the underlying projective structure.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/02a8e08781c076af2fbddbb474fe58e5a0cb8f77
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In Geometry and Topology
Citations in the corpus
- Differential Geometry of Special Mappings (2019, methodology): “87)Let us note that the problem of geodesic mappings onto Riemannian spaces is equivalent to the so-called metrizability, or projective metrizability of a (projective) connection, see [316,388,389]”