Almost hypercomplex manifolds with Hermitian–Norden metrics and 4-dimensional indecomposable real Lie algebras depending on one parameter

Manev, Hristo

doi:10.1007/s00022-021-00580-9

Cited by 2 publications

(1 citation statement)

References 16 publications

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“…Differentiable manifolds M 4n equipped with structures (H, G) = (J 1 , J 2 , J 3 , g, Φ, g 2 , g 3 ) are studied in Refs. [23][24][25][26][27][28] under the name almost hypercomplex pseudo-Hermitian manifolds, almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics, and almost hypercomplex manifolds with Hermitian-Norden metrics, respectively. In this paper we refer to (M 4n , H, G) as an almost hypercomplex manifold with Hermitian-Norden metrics.…”

Section: Cotangent Bundles With Natural Riemann Extensions As Almost ...mentioning

confidence: 99%

Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions

Bejan

Nakova

2022

Mathematics

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The Riemann extension, introduced by E. K. Patterson and A. G. Walker, is a semi-Riemannian metric with a neutral signature on the cotangent bundle T∗M of a smooth manifold M, induced by a symmetric linear connection ∇ on M. In this paper we deal with a natural Riemann extension g¯, which is a generalization (due to M. Sekizawa and O. Kowalski) of the Riemann extension. We construct 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 an almost complex manifold, where the natural Riemann extension g¯ is a Norden metric. We obtain necessary and sufficient conditions for (T∗M,J¯,g¯) to belong to the main classes of the Ganchev–Borisov classification of the almost complex manifolds with Norden metric. We also examine the cases when the base manifold is an almost complex manifold with Norden metric or it is a complex manifold (M,J,∇′) endowed with an almost complex connection ∇′ (∇′J=0). We investigate the harmonicity with respect to g¯ of the almost complex structure J¯, according to the type of the base manifold. Moreover, we define an almost hypercomplex structure (J¯1,J¯2,J¯3) on the cotangent bundle T∗M4n of an almost hypercomplex manifold (M4n,J1,J2,J3,∇) with a symmetric linear connection ∇. The natural Riemann extension g¯ is a Hermitian metric with respect to J¯1 and a Norden metric with respect to J¯2 and J¯3.

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Section: Cotangent Bundles With Natural Riemann Extensions As Almost ...mentioning

confidence: 99%

Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions

Bejan

Nakova

2022

Mathematics

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Lie Groups of Dimension Four and Almost Hypercomplex Manifolds with Hermitian–Norden Metrics

Manev¹

2022

Z. mat. fiz. anal. geom.

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Almost hypercomplex manifolds with Hermitian–Norden metrics and 4-dimensional indecomposable real Lie algebras depending on one parameter

Cited by 2 publications

References 16 publications

Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions

Almost Complex and Hypercomplex Norden Structures Induced by Natural Riemann Extensions

Lie Groups of Dimension Four and Almost Hypercomplex Manifolds with Hermitian–Norden Metrics

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