Journal ArticleDOI
Lie Groups as Four-dimensional Complex Manifolds with Norden Metric
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In this article, two examples of 4-dimensional complex manifolds with Norden metric are constructed by means of Lie groups and Lie algebras, and the form of the curvature tensor for each of the examples is obtained.Abstract:
Two examples of 4-dimensional complex manifolds with Norden metric are constructed by means of Lie groups and Lie algebras. Both manifolds are characterized geometrically. The form of the curvature tensor for each of the examples is obtained. Conditions these manifolds to be isotropic-Kahlerian are given.read more
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Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions
TL;DR: In this paper , the authors considered a generalization of the Riemann extension and constructed an almost complex structure J¯ on the cotangent bundle T ∗M of an almost-complex manifold (M,J,∇) with a symmetric linear connection ∇ such that (T∗M, J¯,g¯) is a almost complex manifold with Norden metric, and obtained necessary and sufficient conditions for J¯ to belong to the main classes of the Ganchev-Borisov classification.
References
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Journal ArticleDOI
Complex Analytic Coordinates in Almost Complex Manifolds
A. Newlander,Louis Nirenberg +1 more
TL;DR: A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations as mentioned in this paper, and a manifold can be called almost complex if there is a linear transformation J defined on the tangent space at every point, and varying differentiably with respect to local coordinates.
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Invariant pseudo Kaehler metrics in dimension four
TL;DR: In this article, Ricci flat unimodular pseudo-Kahler Lie groups are determined and constructed in higher dimension on some ane Lie algebras, and the compatible pairs (J,!) are parametrized up to complex isomorphism (where J is a complex structure and! is a symplectic structure).
Journal ArticleDOI
Non existence of complex structures on filiform lie algebras
Michel Goze,Elisabeth Remm +1 more
TL;DR: In this article, the authors prove the nonexistence of complex structures over nilpotent Lie algebras of maximal class (also called filiform) and show that complex structures are not possible over the maximal class.
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A lie group as a 4-dimensional quasi-k¨ ahler manifold with norden metric
TL;DR: A 4-parametric family of 4-dimensional quasi-Kahler manifolds with Norden metric is constructed on a Lie group in this paper, and the condition for such a 4-manifold to be isotropic is given.