Connections which are harmonic with respect to general natural metrics

@article{Bejan2012ConnectionsWA,
  title={Connections which are harmonic with respect to general natural metrics},
  author={C. L. Bejan and Simona-Luiza Druţǎ-Romaniuc},
  journal={Differential Geometry and Its Applications},
  year={2012},
  volume={30},
  pages={306-317}
}
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13 Citations
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13 Citations

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Harmonic Almost Complex Structures with Respect to General Natural Metrics
We continue here the study initiated in [9] on the harmonicity of certain geometric objects on the total space TM of the tangent bundle of a Riemannian space form (M(c), g). Precisely, in this paper…
Harmonic functions and quadratic harmonic morphisms on Walker spaces
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The projective curvature of the tangent bundle with natural diagonal metric
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Some notes on vector fields in the tangent bundle
Let (M,g)be a Riemannian manifold and T (M) its tangent bundle with the horizontal lift H∇ of the affine connection ∇ of M. The aims of the present paper are to study conditions of infinitesimal…
Laplace, Einstein and Related Equations on D-General Warping
A new concept, namely, D-general warping $$(M=M_1\times M_2,g)$$(M=M1×M2,g), is introduced by extending some geometric notions defined by Blair and Tanno. Corresponding to a result of Tanno in almost…
Problems of Lifts in Symplectic Geometry
Let (M,ω) be a symplectic manifold. In this paper, the authors consider the notions of musical (bemolle and diesis) isomorphisms ωb: TM → T*M and ω#: T*M → TM between tangent and cotangent bundles.…
H-projectively Euclidean Kähler tangent bundles of natural diagonal type By CORNELIA-LIVIA BEJAN and SIMONA-LUIZA DRUŢĂ-ROMANIUC
We obtain the characterization of the natural diagonal Kähler manifolds (TM,G, J) which have constant holomorphic sectional curvature, or equivalently, which are H-projectively Euclidean. Moreover,…
Harmonic metrics on four dimensional non-reductive homogeneous manifolds
We study harmonic metrics with respect to the class of invariant metrics on non-reductive homogeneous four dimensional manifolds. In particular, we consider harmonic lifted metrics with respect to…
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In this paper, we define almost paracontact and normal almost paracontact Finsler structures on a vector bundle and find some conditions for integrability of these structures. We define paracontact…
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References

SHOWING 1-10 OF 20 REFERENCES
On curvatures of linear frame bundles with naturally lifted metrics.
Abstract. We study some simple natural metrics on the linear frame bundle L M over a Riemannian manifold (M, g) which generalize the so-called diagonal metric introduced by K. P. Mok in 1978. We…
General natural Einstein Kähler structures on tangent bundles
On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds
Structure of symmetric tensors of type (0,2) and tensors of type (1,1) on the tangent bundle
The concepts of M-tensor and M-connection on the tangent bundle TM of a smooth manifold M are used in a study of symmetric tensors of type (0, 2) and tensors of type (1, 1) on TM. The constructions…
New structures on the tangent bundles and tangent sphere bundles
In this paper we study a Riemannian metric on the tangent bundle T(M) of a Riemannian manifold M which generalizes Sasaki metric and Cheeger–Gromoll metric and a compatible almost complex structure…
Harmonicity of a foliation and of an associated map
A foliation on a Riemannian manifold (M, g) is harmonic if all the leaves are minimal submanifolds. We give a new characterisation of the harmonicity of a foliation on (M, g) by the harmonicity of an…
Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold
Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$. We classify all natural 0-order vector fields and 2-vector fields on $TM$ generated by…
ON THE DIFFERENTIAL GEOMETRY OF TANGENT BUNDLES OF RIEMANNIAN MANIFOLDS II
H.Poincare used the tangent sphere-bundles of ovaloids in three dimensional Euclidean space, i.e. the phase spaces of the ovaloids, to prove the existence of certain closed geodesies on the ovaloids.…
New structures on tangent bundles
We construct three kinds of almost complex structures compatible with some naturally defined Riemannian metrics on the tangent bundle of an almost Hermitian manifold and in particular, of a complex…
On cotangent bundles of some natural bundles
The author studies relations between the following two types of natural operators: 1. Natural operators transforming vector fields on manifolds into vector fields on a natural bundle $F$; 2. Natural…
...
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