Almost paracontact and parahodge structures on manifolds

Kaneyuki, Soji; Williams, Floyd L.

doi:10.1017/s0027763000021565

Cited by 165 publications

(144 citation statements)

References 8 publications

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“…where X is tangent to M (2n+1) , t is the coordinate on R and f is a C ∞ function on M (2n+1) × R. An almost paracomplex structure J on M (2n+1) × R is defined in [6] by…”

Section: Almost Paracontact Manifoldsmentioning

confidence: 99%

Canonical connections on paracontact manifolds

2008

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Abstract. The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold to be paraSasakian. A Dhomothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is prove 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 a 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.MSC: 53C15, 5350, 53C25, 53C26, 53B30

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“…where X is tangent to M (2n+1) , t is the coordinate on R and f is a C ∞ function on M (2n+1) × R. An almost paracomplex structure J on M (2n+1) × R is defined in [6] by…”

Section: Almost Paracontact Manifoldsmentioning

confidence: 99%

Canonical connections on paracontact manifolds

2008

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“…(ii) the tensor …eld ' induces an almost para-complex structure on the distribution D = ker ; that is, the eigendistributions D + ; D corresponding to the eigenvalues 1, -1 of '; respectively, have equal dimension m: M is said to be almost para-contact manifold if it is endowed with an almost paracontact structure( [7], [16], [19], [26]). …”

Section: Preliminariesmentioning

confidence: 99%

Para-contact product semi-Riemannian submersions

Gündüzalp¹

2017

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. We introduce the concept of para-contact product semi-Riemannian submersions from an almost para-contact metric manifold onto a semi-Riemannian product manifold. We provide an example and show that the vertical and horizontal distributions of such submersions are invariant with respect to the almost para-contact structure of the total manifold. Moreover, we investigate various properties of the O'Neill's tensors of such submersions, …nd the integrability of the horizontal distribution. The paper is also focused on the transference of structures de…ned on the total manifold.

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“…A (2n + 1)-dimensional smooth manifold M is said to be an almost paracontact manifold if it admits an almost paracontact structure (φ, ξ, η), where φ is a (1, 1)-tensor field, ξ a vector field and its dual 1-form η and for any vector field X on M satisfying [15] …”

Section: Preliminaries On (K µ)-Paracontact Metric Manifoldsmentioning

confidence: 99%

Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry

Mandal

2017

B Soc Paran Mat

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The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in (k, µ)-paracontact metric manifolds. We prove the nonexistence of Ricci almost soliton in a (k, µ)-paracontact metric manifold M with k < −1 or k > −1 and whose potential vector field is the Reeb vector field ξ. Further, if the metric g of a (k, µ)-paracontact metric manifold M 2n+1 with k = −1 is a gradient Ricci almost soliton, then we prove that either the manifold is locally isometric to a product of a flat (n + 1)-dimensional manifold and an n-dimensional manifold of negative constant curvature equal to −4, or, M 2n+1 is an Einstein manifold. Finally, an illustrative example is given.

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Almost paracontact and parahodge structures on manifolds

Cited by 165 publications

References 8 publications

Canonical connections on paracontact manifolds

Canonical connections on paracontact manifolds

Para-contact product semi-Riemannian submersions

Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry

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