scholarly journals Almost Contact Metric Structures on 5-Dimensional Nilpotent Lie Algebras

Symmetry ◽  
2016 ◽  
Vol 8 (8) ◽  
pp. 76 ◽  
Author(s):  
Nülifer Özdemir ◽  
Mehmet Solgun ◽  
Şirin Aktay
Keyword(s):  
Lie Algebras ◽  
Nilpotent Lie Algebras ◽  
Almost Contact Metric ◽  
Metric Structures ◽  
Almost Contact Metric Structures

On nonexistence of Kenmotsu structure on аст-hypersurfaces of cosymplectic type of a Kählerian manifold

2019 ◽  
pp. 23-28
Author(s):  
G. Banaru
Keyword(s):  
Hermitian Manifold ◽  
Structural Equations ◽  
Type I ◽  
Almost Hermitian Manifold ◽  
Almost Contact Metric Structure ◽  
Almost Contact Metric ◽  
Contact Metric Structure ◽  
Metric Structures ◽  
Kählerian Manifold ◽  
Almost Contact Metric Structures

Almost contact metric (аст-)structures induced on oriented hypersurfaces of a Kählerian manifold are considered in the case when these аст- structures are of cosymplectic type, i. e. the contact form of these structures is closed. As it is known, the Kenmotsu structure is the most important non-trivial example of an almost contact metric structure of cosymplectic type. The Cartan structural equations of the almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold are obtained. It is proved that an almost contact metric structure of cosymplectic type on a hypersurface of a Kählerian manifold of dimension at least six cannot be a Kenmotsu structure. Moreover, it follows that oriented hypersurfaces of a Kählerian manifold of dimension at least six do not admit non-trivial almost contact metric structures of cosymplectic type that belong to any well studied class of аст-structures. The present results generalize some results on almost contact metric structures on hypersurfaces of an almost Hermitian manifold obtained earlier by V. F. Kirichenko, L. V. Stepanova, A. Abu-Saleem, M. B. Banaru and others.

scholarly journals Coclosed G2-structures inducing nilsolitons

2018 ◽  
Vol 30 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Leonardo Bagaglini ◽  
Marisa Fernández ◽  
Anna Fino
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Nilpotent Lie Algebras ◽  
Almost Complex ◽  
Metric Structures ◽  
Trivial Center ◽  
Nilsoliton Metric

Abstract We show obstructions to the existence of a coclosed {\mathrm{G}_{2}} -structure on a Lie algebra {\mathfrak{g}} of dimension seven with non-trivial center. In particular, we prove that if there exists a Lie algebra epimorphism from {\mathfrak{g}} to a six-dimensional Lie algebra {\mathfrak{h}} , with the kernel contained in the center of {\mathfrak{g}} , then any coclosed {\mathrm{G}_{2}} -structure on {\mathfrak{g}} induces a closed and stable three form on {\mathfrak{h}} that defines an almost complex structure on {\mathfrak{h}} . As a consequence, we obtain a classification of the 2-step nilpotent Lie algebras which carry coclosed {\mathrm{G}_{2}} -structures. We also prove that each one of these Lie algebras has a coclosed {\mathrm{G}_{2}} -structure inducing a nilsoliton metric, but this is not true for 3-step nilpotent Lie algebras with coclosed {\mathrm{G}_{2}} -structures. The existence of contact metric structures is also studied.

scholarly journals Almost contact metric structures induced by $G_2$ structures

2017 ◽  
Vol 41 ◽  
pp. 1072-1086 ◽  
Author(s):  
Nülifer ÖZDEMİR ◽  
Mehmet SOLGUN ◽  
Şirin AKTAY
Keyword(s):  
Almost Contact Metric ◽  
Metric Structures ◽  
Almost Contact Metric Structures

scholarly journals Classification of contact structures associated with the CR-structure of the complex indicatrix

2017 ◽  
Vol 25 (1) ◽  
pp. 163-176
Author(s):  
Elena Popovici
Keyword(s):  
Fixed Point ◽  
Tangent Bundle ◽  
Contact Structure ◽  
Contact Structures ◽  
Cr Structure ◽  
Almost Contact Metric ◽  
Metric Structures ◽  
Pseudo Convex ◽  
Almost Contact Metric Structures

Abstract By regarding the complex indicatrix as an embedded CR-hypersurface of the holomorphic tangent bundle in a fixed point, we analyze some aspects of the relations between its CR structure and the considered contact structure. Moreover, using the classification of the almost contact metric structures associated with a strongly pseudo-convex CR-structure, of D. Chinea and C. Gonzales, we determine the classes corresponding to the natural contact structure of the complex indicatrix and the new structures obtained under a gauge transformation.

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