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Register a new userThe harmonicity of nearly cosymplectic structures
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Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold and prove curvature identities which imply the harmonicity of their parametrizing section, thus complementing earlier results on nearly-K{a}hler almost complex structures.
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We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of the Riemann curvature tensor and find conditions relating the harmonicity of the almost contact and almost complex structures of the total and base spaces of the Morimoto fibration.
The aim of this paper is to introduce a cosymplectic analouge of conformal connection in a cosymplectic manifold and proved that if cosymplectic manifold M admits a cosymplectic conformal connection which is of zero curvature, then the Bochner curvature tensor of M vanishes.
In some other context, the question was raised how many nearly Kahler structures exist on the sphere $S^6$ equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue $lambda = 12$ of the Laplacian acting on 2-forms. A similar result concerning nearly parallel $G_2$-structures on the round sphere $S^7$ holds, too. An alternative proof by Riemannian Killing spinors is also indicated.
We study the space of nearly K{a}hler structures on compact 6-dimensional manifolds. In particular, we prove that the space of infinitesimal deformations of a strictly nearly K{a}hler structure (with scalar curvature scal) modulo the group of diffeomorphisms, is isomorphic to the space of primitive co-closed (1,1)-eigenforms of the Laplace operator for the eigenvalue 2scal/5.
In this paper, we deal with harmonic metrics with respect to generalized Kantowski-Sachs type spacetime metrics. We also consider the Sasaki, horizontal and complete lifts of generalized Kantowski-Sachs type spacetime metrics to tangent bundle and study their harmonicity.
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