In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae...In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.展开更多
In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some...In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some very special cases,the coset space G×G/△(K)carries at least two invariant Einstein metrics.Furthermore,in the case that G1,G2 and K are simple Lie groups,with K■G1,K■G2,and G_1≠G2,such that G_1/K and G2/K are compact isotropy irreducible spaces,we give a complete classification of invariant Einstein metrics on the coset space G1×G2/△(K).展开更多
基金supported by NSFC (12071228,11901300, 51535008)Natural Science Research of Jiangsu Education Institutions of China (19KJB110015)。
文摘In this paper, we consider a class of left invariant Riemannian metrics on Sp(n),which is invariant under the adjoint action of the subgroup Sp(n-3) × Sp(1) × Sp(1) × Sp(1).Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gr?bner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.
基金supported by National Natural Science Foundation of China(Grant Nos.11401425,11626134,11701300,11671212 and 51535008)K.C.Wong Magna Fund in Ningbo University。
文摘In this paper,we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands.We show that,if G/K is a compact isotropy irreducible space with G and K simple,then except for some very special cases,the coset space G×G/△(K)carries at least two invariant Einstein metrics.Furthermore,in the case that G1,G2 and K are simple Lie groups,with K■G1,K■G2,and G_1≠G2,such that G_1/K and G2/K are compact isotropy irreducible spaces,we give a complete classification of invariant Einstein metrics on the coset space G1×G2/△(K).
