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Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on -entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic...
On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.
We investigate ∇-flat and pointwise-∇-flat functions on affine and Riemannian manifolds. We show that the set of all ∇-flat functions on (M,∇) is a ring which has interesting properties similar to the ring of polynomial functions.
The object of the present paper is to study -Ricci solitons on -Einstein -manifolds. It is shown that if is a recurrent torse forming -Ricci soliton on an -Einstein -manifold then is (i) concurrent and (ii) Killing vector field.
In this paper we study vector fields in Riemannian spaces, which satisfy , , We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and -vector fields cannot exist simultaneously. It was found that Riemannian spaces with -vector fields of constant length have constant scalar curvature. The conditions for the existence of -vector fields in symmetric spaces are given....
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