Canonical connections on paracontact manifolds
By Simeon Zamkovoy. 2007
311 citations recorded by the source corpus.
The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A $${\mathcal{D}}$$ -homothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is proved that their scalar curvature is a constant, and it is shown that in the paraSasakian case these spaces can be obtained from Einstein paraSasakian manifolds with $${\mathcal{D}}$$ -homothetic transformations. It is shown that an almost paracontact structure admits a connection with totally skew-symmetric torsion if and only if the Nijenhuis tensor of the paracontact structure is skew-symmetric and the defining vector field is Killing.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/a515a8a4569dd103aaf6e49099330042e10e29f4
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Citations in the corpus
- Slant Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds (2012, unknown): “4) A 3-dimensional normal almost paracontact metric manifold is said to be • paracosymplectic if α = β = 0 [10], • quasi-para-Sasakian if and only if α = 0 and β = 0 [14,22], • β-para-Sasakian if and only if α = 0 and β = 0 and β is constant, in particular, para-Sasakian if β = −1 [22,23], • α-para-”
- On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds (2009, background): “said to be normal (cf. [9] and recent papers [3, 11 ]).”
- Geometry of $H$-paracontact metric manifolds (2013, background): “As shown in [22], any almost paracontact metric manifold (M2n+ 1, φ, ξ, η, g) admits a φ-basis, that is, a local orthonormal basis of the form {ξ, e1, .”
- The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structure (2014, background): “ X,Y is a basis of a non-degenerate section σ. 4. Almost(para) contact metricmanifolds In the geometric literature, we find various classes of almost contact or paracontact metric structures; see e.g. [6, 7, 8, 10, 13, 29, 32], etc. The following convention unifying both the contact and paracontact n”
- Nullity conditions in paracontact geometry (2012, background): “One can easily check that the new structure (φ̄, ξ̄, η̄, ḡ) is still a paracontact metric structure ([25]).”