Volume-preserving geodesic symmetries on four-dimensional Kähler manifolds

Unit Tangent Sphere Bundles with Constant Scalar Curvature

“…We only need condition (22) to prove the lemma. We note beforehand that by the second Bianchi identity we have…”

Singer-Thorpe bases for special Einstein curvature tensors in dimension 4

“…, e 4 } is an ST basis compatible with the given orientation. Then, the following fact is also well known ( [6], [8]): Proposition 1.7. Let (V, , , R) be an Einstein triplet.…”

“…The following theorem is a reformulation and we put it here for the completeness of the exposition. Because it is based on Proposition 3.5, it is useful also as an alternative proof of Lemma 5 in [8]. For completeness, we end this paragraph by the observation that the conditions of type G together with the conditions of type H imply conditions…”

“…We also remark that the Einstein curvature tensor satisfying all conditions of the type G i , or H i , is a 2-stein curvature tensor (see formulas (1.2)). ST bases of 2-stein curvature tensors were studied in [8], see Lemma 5 there. The following theorem is a reformulation and we put it here for the completeness of the exposition.…”

On inaudible curvature properties of closed Riemannian manifolds

“…In dimension four, partial classifications were obtained by J.T. Cho, K. Sekigawa and L. Vanhecke [22], [23], [8]; the classification of 4-dimensional homogeneous D'Atri spaces has recently been completed by the first author and O. Kowalski [1], [2], [3]. See [17] for references about D'Atri spaces and related topics.…”