44 citations · 76 across the 22 of their papers we have counts for
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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…
Jacobi--Tsankov manifolds which are not 2-step nilpotent
M. Brozos-Vazquez, P. Gilkey
An algebraic curvature tensor A is said to be Jacobi-Tsankov if J(x)J(y)=J(y)J(x) for all x,y. This implies J(x)J(x)=0 for all x; necessarily A=0 in the Riemannian setting. Further…
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…
Ranking Participants in Tournaments by means of Rating Functions
M. Brozos-Vazquez, M. A. Campo-Cabana, J. C. Diaz-Ramos +1
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a gi…