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The Riemann extensions with cyclic parallel Ricci tensor

Mathematische Nachrichten, 2014
The property of being a D'Atri space (i.e., a Riemannian manifold with volume‐preserving geodesic symmetries) is equivalent, in the real analytic case, to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold satisfying the first odd Ledger condition L3 is said to be an L3‐space.
Oldrich Kowalski
exaly   +3 more sources

Critical metrics with cyclic parallel Ricci tensor for volume functional on manifolds with boundary

Geometriae Dedicata, 2018
In this paper, the authors study the critical metrics with cyclic parallel Ricci tensor for volume functional on compact manifolds \((M^n,g)\), \((n\ge 3)\), with boundary \(\partial M\). A Riemannian metric \(g\) is said to be with cyclic parallel Ricci tensor if its Ricci tensor satisfies \(\nabla_X \mathrm{Ric}(Y,Z)+\nabla_Y \mathrm{Ric}(Z,X ...
Sheng, Weimin, Wang, Lisheng
exaly   +3 more sources

Real Hypersurfaces in ℂP 2 and ℂH 2 with Cyclic Parallel ∗-Ricci Tensor

Studia Scientiarum Mathematicarum Hungarica, 2021
In this paper, we prove that the ∗-Ricci tensor of a real hypersurface in complex projective plane ℂP 2 or complex hyperbolic plane ℂH 2 is cyclic parallel if and only if the hypersurface is of type (A). We find some three-dimensional real hypersurfaces having non-vanishing and non-parallel ∗-Ricci tensors which are cyclic
Yaning Wang, Wenjie Wang
openaire   +1 more source