Displaying similar documents to “On the geometry of some solvable extensions of the Heisenberg group”

On the geometrical properties of Heisenberg groups

Mehri Nasehi (2020)

Archivum Mathematicum

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In [20] the existence of major differences about totally geodesic two-dimensional foliations between Riemannian and Lorentzian geometry of the Heisenberg group H 3 is proved. Our aim in this paper is to obtain a comparison on some other geometrical properties of these spaces. Interesting behaviours are found. Also the non-existence of left-invariant Ricci and Yamabe solitons and the existence of algebraic Ricci soliton in both Riemannian and Lorentzian cases are proved. Moreover, all of...

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2014)

Czechoslovak Mathematical Journal

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Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces M of Type ( A ) in complex two plane Grassmannians G 2 ( ℂ m + 2 ) with a commuting condition between the shape operator A and the structure tensors φ and φ 1 for M in G 2 ( ℂ m + 2 ) . Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator A and a new operator φ φ 1 induced by two structure tensors φ and φ 1 . That is, this commuting shape operator is given by φ φ 1 A = A φ φ 1 . Using this condition, we...

φ ( Ric ) -vector fields in Riemannian spaces

Irena Hinterleitner, Volodymyr A. Kiosak (2008)

Archivum Mathematicum

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In this paper we study vector fields in Riemannian spaces, which satisfy ∇ ϕ = μ , 𝐑𝐢𝐜 , μ = const. We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and ϕ ( Ric ) -vector fields cannot exist simultaneously. It was found that Riemannian spaces with ϕ ( Ric ) -vector fields of constant length have constant scalar curvature. The conditions for the existence of ϕ ( Ric ) -vector fields in symmetric spaces...

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...

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2012)

Czechoslovak Mathematical Journal

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In this paper, first we introduce a new notion of commuting condition that φ φ 1 A = A φ 1 φ between the shape operator A and the structure tensors φ and φ 1 for real hypersurfaces in G 2 ( ℂ m + 2 ) . Suprisingly, real hypersurfaces of type ( A ) , that is, a tube over a totally geodesic G 2 ( ℂ m + 1 ) in complex two plane Grassmannians G 2 ( ℂ m + 2 ) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G 2 ( ℂ m + 2 ) satisfying the commuting condition. Finally we get a characterization of Type ( A ) in terms of such...

Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces

Ryszard Deszcz, Malgorzata Głogowska (2002)

Colloquium Mathematicae

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We construct a class of nonsemisymmetric Ricci-semisymmetric warped products. Some manifolds of this class can be locally realized as hypersurfaces of a semi-Euclidean space s n + 1 , n ≥ 5.