1,335 research outputs found
The geometry of modified Riemannian extensions
We show that every paracomplex space form is locally isometric to a modified
Riemannian extension and give necessary and sufficient conditions so that a
modified Riemannian extension is Einstein. We exhibit Riemannian extension
Osserman manifolds of signature (3,3) whose Jacobi operators have non-trivial
Jordan normal form and which are not nilpotent. We present new four dimensional
results in Osserman geometry
Ricci Solitons on Lorentzian Manifolds with Large Isometry Groups
We show that Lorentzian manifolds whose isometry group is of dimension at
least are expanding, steady and shrinking Ricci solitons
and steady gradient Ricci solitons. This provides examples of complete locally
conformally flat and symmetric Lorentzian Ricci solitons which are not rigid
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