Abstract. In this paper, we study invariant Einstein metrics on Ledger -Obata spaces F m / diag(F ). In particular, we classify invariant Einstein metrics on F 4 / diag(F ) and estimate the number of invariant Einstein metrics on Ledger -Obata spaces F m / diag(F ).2010 Mathematical Subject Classification: 53C25 (primary), 53C30, 17B20 (secondary).
In the paper we obtain an explicit formula for the intrinsic diameter of the surface of a rectangular parallelepiped in 3-dimensional Euclidean space. As a consequence, we prove that an parallelepiped with relation 1 : 1 : √ 2 for its edge lengths has maximal surface area among all rectangular parallelepipeds with given intrinsic diameter.
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