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On canonical screen for lightlike submanifolds of codimension two

K. Duggal (2007)

Open Mathematics

In this paper we study two classes of lightlike submanifolds of codimension two of semi-Riemannian manifolds, according as their radical subspaces are 1-dimensional or 2-dimensional. For a large variety of both these classes, we prove the existence of integrable canonical screen distributions subject to some reasonable geometric conditions and support the results through examples.

On compact astheno-Kähler manifolds

Koji Matsuo, Takao Takahashi (2001)

Colloquium Mathematicae

We prove that every compact balanced astheno-Kähler manifold is Kähler, and that there exists an astheno-Kähler structure on the product of certain compact normal almost contact metric manifolds.

On compact holomorphically pseudosymmetric Kählerian manifolds

Zbigniew Olszak (2009)

Open Mathematics

For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem....

On compact homogeneous symplectic manifolds

P. B. Zwart, William M. Boothby (1980)

Annales de l'institut Fourier

In this paper the authors study compact homogeneous spaces G / K (of a Lie group G ) on which there if defined a G -invariant symplectic form Ω . It is an important feature of the paper that very little is assumed concerning G and K . The essential assumptions are: (1) G is connected and (2) K is uniform (i.e., G / K is compact). Further, for convenience only and with no loss of generality, it is supposed that G is simply connected and K contains no connected normal subgroup of G , i.e., that G acts almost effectively...

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