摘要
A-manifolds and B-manifolds, introduced by Gray(1978), are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6,m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.
A-manifolds and/3-manifolds, introduced by Gray （1978）, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an A-manifold and a B-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with g = 4 distinct principal curvatures are A-manifolds. As for the focal submanifolds with g = 6, m = 1 or 2, only one is an A-manifold, and neither is a B-manifold.
基金
supported by National Natural Science Foundation of China(Grant No.11301027)
the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130003120008)
the Beijing Natural Science Foundation(Grant No.1144013)
the Fundamental Research Funds for the Central Universities(Grant No.2012CXQT09)
