Vertical sectional curvature and K-contactness

Rukimbira, Philippe

doi:10.1007/bf01224048

Cited by 11 publications

(16 citation statements)

References 4 publications

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“…Suppose (M, η, ω) is a K-cosymplectic manifold and let ḡ be a metric for which ξ is Killing. Following [39], we show how to construct an adapted metric g for which ξ is Killing. As a byproduct, we will also get a tensor φ such that (η, ξ, φ, g) is K-cosymplectic with Kähler form ω, proving basically that a K-cosymplectic manifold (M, η, ω) with an adapted Riemannian metric g for which ξ is Killing carries a K-cosymplectic structure.…”

Section: Given a Tensormentioning

confidence: 99%

K-Cosymplectic manifolds

Bazzoni

Goertsches

2014

Ann Glob Anal Geom

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In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemannian metric. These structures generalize coKähler structures, in the same way as K-contact structures generalize Sasakian structures. In analogy to the contact case, we distinguish between (quasi-)regular and irregular structures; in the regular case, the K-cosymplectic manifold turns out to be a flat circle bundle over an almost Kähler manifold. We investigate de Rham and basic cohomology of K-cosymplectic manifolds, as well as cosymplectic and Hamiltonian vector fields and group actions on such manifolds. The deformations of type I and II in the contact setting have natural analogues for cosymplectic manifolds; those of type I can be used to show that compact K-cosymplectic manifolds always carry quasi-regular structures. We consider Hamiltonian group actions and use the momentum map to study the equivariant cohomology of the canonical torus action on a compact K-cosymplectic manifold, resulting in relations between the basic cohomology of the characteristic foliation and the number of closed Reeb orbits on an irregular K-cosymplectic manifold.

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Section: Given a Tensormentioning

confidence: 99%

K-Cosymplectic manifolds

Bazzoni

Goertsches

2014

Ann Glob Anal Geom

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“…The case rk(M, η) = 1 is the quasi-regular case, while the other extreme rk(M, η) = n+1 is the toric case studied in [BM1,BM2,BG3]. Furthermore, Rukimbira [Ruk1] showed that one can approximate any K-contact form η by a sequence of quasi-regular K-contact forms in the same contact structure. Thus, every K-contact manifold has an η of rank 1.…”

Section: The Leaf Closures Of F ξmentioning

confidence: 99%

Einstein manifolds and contact geometry

Boyer

Galicki

2001

Proc. Amer. Math. Soc.

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“…A result of [23] says that if M admits a Sasakian structure, then it admits also a quasi-regular Sasakian structure. Also, if a compact manifold M admits a K-contact structure, it admits a quasi-regular contact structure [21].…”

Section: K-contact and Sasakian 5-manifoldsmentioning

confidence: 99%

Homology Smale–Barden Manifolds with K-contact but not Sasakian Structures

Muñoz

Rojo

Tralle

2018

International Mathematics Research Notices

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Kollár has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In particular, we find the first example of a closed 5-manifold M with H 1 (M, Z) = 0 which is K-contact but which carries no semi-regular Sasakian structures.2010 Mathematics Subject Classification. 53C25, 53D35, 57R17, 14J25.

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Vertical sectional curvature and K-contactness

Cited by 11 publications

References 4 publications

K-Cosymplectic manifolds

K-Cosymplectic manifolds

Einstein manifolds and contact geometry

Homology Smale–Barden Manifolds with K-contact but not Sasakian Structures

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