# 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} }

## 13 Citations

Harmonic Almost Complex Structures with Respect to General Natural Metrics

- Mathematics
- 2014

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

- Mathematics
- 2016

Abstract: Let (W, q,D) be a 4-dimensional Walker manifold. After providing a characterization and some examples for several special (1, 1)-tensor fields on (W, q,D) , we prove that the proper almost…

The projective curvature of the tangent bundle with natural diagonal metric

- Mathematics
- 2015

Our study is mainly devoted to a natural diagonal metric $G$ on the total space $TM$ of the tangent bundle of a Riemannian manifold $(M,g)$. We provide the necessary and sufficient conditions under…

Structures Which are Harmonic with Respect to Walker Metrics

- Mathematics
- 2015

Let $${(W, q, \mathcal{D})}$$(W,q,D) be a Walker manifold. We find all Walker metrics which are harmonic [in the sense of Chen and Nagano in (J Math Soc Jpn 36:295–313, 1984)] w.r.t. q. On the total…

Some notes on vector fields in the tangent bundle

- Mathematics
- 2019

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

- MathematicsMediterranean Journal of Mathematics
- 2019

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

- MathematicsChinese Annals of Mathematics, Series B
- 2019

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

- Mathematics
- 2016

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

- Mathematics
- 2018

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…

Almost Paracontact Finsler Structures on Vector Bundle

- Mathematics
- 2013

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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