Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds
Mancho Manev,Veselina Tavkova +1 more
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In this paper, almost paracontact Riemannian manifolds of the lowest dimension 3 were constructed on a family of Lie groups and the obtained manifolds were studied. And the Curvature properties of these manifolds are investigated.Abstract:
Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds are investigated. An example is commented as support of the obtained results.read more
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Matrix Lie Groups as 3-Dimensional Almost Paracontact Almost Paracomplex Riemannian Manifolds
Mancho Manev,Veselina Tavkova +1 more
TL;DR: In this article, a correspondence between the Lie algebra and the explicit matrix representation of a Lie group is established for Riemannian RiemANNs, where the Lie groups are considered as three-dimensional almost paracontact almost-paracomplex Riemmannian manifolds.
Journal ArticleDOI
Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure
Hristo Manev,Mancho Manev +1 more
TL;DR: In this article, a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure was introduced and studied.
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Almost hypercomplex manifolds with Hermitian–Norden metrics and 4-dimensional indecomposable real Lie algebras depending on one parameter
TL;DR: In this paper, the authors studied almost hypercomplex structure with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds, and studied the geometrical characteristics of the respective almost hyper-complex manifolds.
Posted Content
Almost hypercomplex manifolds with Hermitian-Norden metrics and 4-dimensional indecomposable real Lie algebras depending on two parameters
TL;DR: In this paper, the authors investigated almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds, and studied both the basic classes of a classification of four-dimensional indecomposable real Lie algebras depending on two parameters.
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Para-Ricci-like Solitons with Vertical Potential on Para-Sasaki-like Riemannian Π-Manifolds
TL;DR: In this article, the potential of a para-Ricci-like soliton on Riemannian Π-manifolds is investigated and some additional geometric properties of the constructed objects are proven.
References
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TL;DR: In this paper, the authors classify invariant hypercomplex structures on a 4-dimensional real Lie group G. The purpose of the purpose of this paper is to classify invariants on the real and complex hyperbolic spaces RH4 and CH2, respectively.
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TL;DR: In this paper, the authors studied hyperKahler torsion structures on nilpotent Lie groups and on associated nilmanifolds and showed that the corresponding hypercomplex structures are of a special kind called Abelian.
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