A selfsimilar Hessian manifold with a potential homothetic vector field is locally a product of radiant Hessian manifolds, each described by a single homogeneous potential function.
Geometry and holonomy of indecomposable cones
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non irreducible cones. The latter admit a parallel distribution of null $k$-planes, and we study the cases $k=1$ and $k=2$ in detail. In these cases, i.e., when the cone admits a distribution of parallel null tangent lines or planes, we give structure theorems about the base manifold. Moreover, in the case $k=1$ and when the base manifold is Lorentzian, we derive a description of the cone holonomy. This result is obtained by a computation of certain cocycles of indecomposable subalgebras in $\mathfrak{so}(1,n-1)$.
fields
math.DG 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Selfsimilar Hessian manifolds
A selfsimilar Hessian manifold with a potential homothetic vector field is locally a product of radiant Hessian manifolds, each described by a single homogeneous potential function.