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.

Classification of 4 -dimensional homogeneous weakly Einstein manifolds

Teresa Arias-Marco, Oldřich Kowalski (2015)

Czechoslovak Mathematical Journal

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Y. Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A. Gray and T. J. Willmore in the context of mean-value theorems in Riemannian geometry. The dimension 4 is the most interesting...

Metrics with homogeneous geodesics on flag manifolds

Dimitri V. Alekseevsky, Andreas Arvanitoyeorgos (2002)

Commentationes Mathematicae Universitatis Carolinae

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A geodesic of a homogeneous Riemannian manifold ( M = G / K , g ) is called homogeneous if it is an orbit of an one-parameter subgroup of G . In the case when M = G / H is a naturally reductive space, that is the G -invariant metric g is defined by some non degenerate biinvariant symmetric bilinear form B , all geodesics of M are homogeneous. We consider the case when M = G / K is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group G , and we give a simple necessary condition that M admits a non-naturally...

On blocks of arithmetic progressions with equal products

N. Saradha (1997)

Journal de théorie des nombres de Bordeaux

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Let f ( X ) ∈ ℚ [ X ] be a monic polynomial which is a power of a polynomial g ( X ) ∈ ℚ [ X ] of degree μ ≥ 2 and having simple real roots. For given positive integers d 1 , d 2 , ℓ , m with ℓ < m and gcd ( ℓ , m ) = 1 with μ ≤ m + 1 whenever m < 2 , we show that the equation f ( x ) f ( x + d 1 ) ⋯ f ( x + ( ℓ k - 1 ) d 1 ) = f ( y ) f ( y + d 2 ) ⋯ f ( y + ( m k - 1 ) d 2 ) with f ( x + j d 1 ) ≠ 0 for 0 ≤ j < ℓ k has only finitely many solutions in integers x , y and k ≥ 1 except in the case m = μ = 2 , ℓ = k = d 2 = 1 , f ( X ) = g ( X ) , x = f ( y ) + y .