An [eta]-Einstein manifold
with [beta] vanishing and [alpha] a constant is obviously an Einstein manifold
M] is a steady Einstein manifold
with Killing V and [bar.
n],g), n = dimM [greater than or equal to] 2, is said to be an Einstein manifold
if the Ricci tensor S is given by
Then either [alpha] = [+ or -] [beta] or M is an Einstein manifold
in which case the curvature is given by r = n(n - 1)[epsilon]([epsilon][[alpha].
Next we define a semi-Einstein manifold
which is the generalization of Einstein manifold
2) N is an Einstein manifold
and the positive function [phi] = [f.
2] - [sigma]) or, S = - 2ng which implies that the LP-Sasakian manifold is an Einstein manifold
In particular, M' is an Einstein manifold
with zero scalar curvature and by Sekigawa theorem () J' is parallel.
An n-dimensional Riemannian manifold (M,g), n > 2, is said to be an Einstein manifold
if its Ricci tensor S satisfies the condition S = r/n g, where r denotes the scalar curvature of M.
2m+1] (c); c > -3 with positive sectional curvature is Einstein manifold
3]) = 0, then the manifold reduces to an Einstein manifold
This shows that Riemannian manifold is an Einstein manifold