We show every toric Sasaki–Einstein manifold S admits a special Legendrian submanifold L which arises as the link fix(τ) ∩ S of the fixed point set fix(τ) of an anti-holomorphic involution τ on the cone C(S). In particular, we obtain a special Legendrian torus S × S in an irregular toric Sasaki–Einstein manifold which is diffeomorphic to S × S. Moreover, there exists a special Legendrian subman...

On any given compact manifold M with boundary ∂M , it is proved that the moduli space E of Einstein metrics on M is a smooth, infinite dimensional Banach manifold. The Dirichlet and Neumann boundary maps to data on ∂M are smooth Fredholm maps of index 0. These results also hold for manifolds with compact boundary which have a finite number of locally asymtotically flat ends, as well as for the ...

We give an elementary treatment of the existence of complete Kähler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n + 1)-sphere. Mathematics Subject Classification (2000) 53C

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.

The notion of coupled Kähler–Einstein metrics was introduced recently by Hultgren–Witt Nyström. In this paper we discuss deformation a metric on Fano manifold. We obtain necessary and sufficient condition for to be deformed another manifold admitting non-trivial holomorphic vector fields. addition also Käher–Einstein when the complex structure varies.

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally ...

In this paper, we initiate the study of a generalized soliton on Riemannian manifold, find characterization for Euclidean space, and in compact case, sufficient condition under which it reduces to quasi-Einstein manifold. We also conditions an Einstein Note that Ricci solitons being self-similar solutions heat flow, topic is related symmetry geometry manifolds. Moreover, generalizations are nat...

Abstract We prove that every compact, homogeneous $$\eta $$ η -Einstein almost cosymplectic manifold is a manifold.