6 research outputs found
The geometry of modified Riemannian extensions
Full text linkWe 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
Intrinsic and extrinsic geometry of hypersurfaces in \varvec{\mathbb {S}}^{\varvec{n}} \varvec{\times } \varvec{\mathbb {R}} S n × R and \varvec{\mathbb {H}}^{\varvec{n}}\varvec{\times } \varvec{\mathbb {R}} H n × R
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