Displaying similar documents to “Some examples of homogeneous Einstein manifolds”

Homogeneous Einstein metrics on Stiefel manifolds

Andreas Arvanitoyeorgos (1996)

Commentationes Mathematicae Universitatis Carolinae

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A Stiefel manifold V k 𝐑 n is the set of orthonormal k -frames in 𝐑 n , and it is diffeomorphic to the homogeneous space S O ( n ) / S O ( n - k ) . We study S O ( n ) -invariant Einstein metrics on this space. We determine when the standard metric on S O ( n ) / S O ( n - k ) is Einstein, and we give an explicit solution to the Einstein equation for the space V 2 𝐑 n .

Some dimensional results for a class of special homogeneous Moran sets

Xiaomei Hu (2016)

Czechoslovak Mathematical Journal

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We construct a class of special homogeneous Moran sets, called { m k } -quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of { m k } k ≥ 1 , we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works.

Naturally reductive homogeneous ( α , β ) -metric spaces

M. Parhizkar, H.R. Salimi Moghaddam (2021)

Archivum Mathematicum

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In the present paper we study naturally reductive homogeneous ( α , β ) -metric spaces. We show that for homogeneous ( α , β ) -metric spaces, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space, given in the literature, are equivalent. Then, we compute the flag curvature of naturally reductive homogeneous ( α , β ) -metric spaces.