17 citations · 115 across the 49 of their papers we have counts for
5 papers · 2 filters
Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey
Let J be a unitary almost complex structure on a Riemannian manifold (M,g). If x is a unit tangent vector, let P be the associated complex line spanned by x and by Jx. We show that…
Algebraic theory of affine curvature tensors
N. Blazic, P. Gilkey, S. Nikcevic +1
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsio…
The global geometry of Riemannian manifolds with commuting curvature operators
M. Brozos-Vazquez, P. Gilkey
We give manifolds in both the Riemannian and in the higher signature settings whose Riemann curvature operators commute, i.e. which satisfy R(a,b)R(c,d)=R(c,d)R(a,b) for all tangen…
Pseudo-Riemannian manifolds with Commuting Jacobi Operators
M. Brozos-Vazquez, P. Gilkey
We study the geometry of pseudo-Riemannian manifolds which are Jacobi--Tsankov, i.e. J(x)J(y)=J(y)J(x) for all tangent vectors x and y. We also study manifolds which are 2-step Jac…
Puffini-Videv Models and Manifolds
P. Gilkey, E. Puffini, V. Videv
Let be the higher order Jacobi operator. We study algebraic curvature tensors where . In the Riemannian setting, we give a complete charac…