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We study the Riemannian geometry of contact manifolds with respect to a fixed admissible metric, making the Reeb vector field unitary and orthogonal to the contact distribution, under the assumption that the Levi–Tanaka form is parallel with respect to a canonical connection with torsion. 相似文献
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Beniamino Cappelletti Montano Antonio De Nicola Giulia Dileo 《Annals of Global Analysis and Geometry》2008,33(4):397-409
In the present article we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular, we prove that the three
Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation.
Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that
3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting
theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the
vertical distribution is a minimum of the corrected energy.
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We prove that any simply connected
-manifold of CR-codimension s 2 is noncompact by showing that the
complete, simply connected
-manifolds are all the CR products N × {s-1} with N Sasakian, endowed with a
suitable product metric. N is a Sasakian -symmetric space if and only if M is CR-symmetric. The locally CR-symmetric
-manifolds are characterized by
=0 where
is the Tanaka--Webster connection. This characterization is showed to be nonvalid for nonnormal almost
-manifolds.Mathematics Subject Classifications (2000). 53C25, 53C35, 32V05. 相似文献
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We consider almost Kenmotsu manifolds (M2n+1,φ,ξ,η,g) with η-parallel tensor h′=h○φ, 2h being the Lie derivative of the structure tensor φ with respect to the Reeb vector field ξ. We describe the Riemannian geometry of an integral submanifold of the distribution orthogonal to ξ, characterizing the CR-integrability of the structure. Under the additional condition ξh′=0, the almost Kenmotsu manifold is locally a warped product. Finally, some lightlike structures on M2n+1 are introduced and studied. 相似文献
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Beniamino Cappelletti Montano Antonio De Nicola Giulia Dileo 《Annals of Global Analysis and Geometry》2009,35(4):445-448
We correct the results in section 6 of [B. Cappelletti Montano, A. De Nicola, G. Dileo, 3-Quasi-Sasakian manifolds, Ann. Global
Anal. Geom. 33 (2008), 397–409], concerning the corrected energy of the Reeb distribution of a compact 3-quasi-Sasakian manifold.
The results are slightly different than what was originally claimed and they are obtained by using results in [B. Cappelletti
Montano, A. De Nicola, G. Dileo, The geometry of a 3-quasi-Sasakian manifold, Int. J. Math., to appear, arXiv:0801.1818],
where the geometry of these manifolds is more deeply investigated.
The online version of the original article can be found under doi:. 相似文献
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Agricola Ilka Dileo Giulia Stecker Leander 《Annals of Global Analysis and Geometry》2021,60(1):111-141
Annals of Global Analysis and Geometry - We show that every 3- $$(\alpha ,\delta )$$ -Sasaki manifold of dimension $$4n + 3$$ admits a locally defined Riemannian submersion over a quaternionic... 相似文献
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We introduce the notion of abelian almost contact structures on an odd-dimensional real Lie algebra . We investigate correspondences with even-dimensional Lie algebras endowed with an abelian complex structure, and with Kähler Lie algebras when carries a compatible inner product. The classification of 5-dimensional Sasakian Lie algebras with abelian structure is obtained. Later, we introduce abelian almost 3-contact structures on real Lie algebras of dimension , obtaining the classification of these Lie algebras in dimension 7. Finally, we deal with the geometry of a Lie group G endowed with a left invariant abelian almost 3-contact metric structure. We determine conditions for G to admit a canonical metric connection with skew torsion, which plays the role of the Bismut connection for hyperKähler with torsion (HKT) structures arising from abelian hypercomplex structures. We provide examples and discuss the parallelism of the torsion of the canonical connection. 相似文献
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