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1

Complete lift of Fa(K,1) structure in the tangent bundle

Upreti J.

Demonstratio Mathematica

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2008

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Vol. 41, nr 4

915-920

EN

Prasad and Gupta have obtained the integrability conditions of a-structure. In the present paper I have studied the complete lift of - structure in the tangent bundle.

2

Horizontal and complete lift of Fa(K,1)-structure in the tangent bundle

Prasad C., Chauhan P.

Demonstratio Mathematica

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2007

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Vol. 40, nr 2

441-448

EN

Prasad and Gupta [2] have obtained the integrability conditions of a structure satisfying FK -a2F = 0. The complete lift of Flambda-structure in tangent bundle was studied by Awasthi and Gupta [1]. In the present paper, we have studied the horizontal & complete lifts of Fa(K, 1)-structure in the tangent bundle.

3

Some geometric structures on the tangent bundle of a Riemannian manifold

Papaghiuc N.

Demonstratio Mathematica

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2004

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Vol. 37, nr 1

215--228

EN

It is defined a new almost complex structure with Norden metric (hyperbolic metric) on the tangent bundle TM of an n- dimensional Riemannian manifold M. Next, the conditions under which the considered almost complex structure with Norden metric belongs to one of the eight classes of almost complex manifolds with Norden metric obtained by G. T. Ganchev and D. V. Borisov in the classification from [2] there are studied.

4

A framed f(3,-1) structure on the tangent bundle of a lagrange space

Gîrţu M.

Demonstratio Mathematica

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2004

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Vol. 37, nr 4

955--961

EN

For a tangent bundle (TM,r,M), the kernel of the differential r* of the projection r defines the vertical subbundle VTM of the bundle (TTM, rTM , TM). A supplement HTM of it is called a horizontal subbundle or a nonlinear connection on M, (R. Miron and M. Anastasiei, [5]). The direct decomposition TTM = HTM VTM gives rise to a natural almost product structure P on the manifold TM. A general method to associate to P a framed f(3, -l)-structure of any corank is pointed out. When we endow M with a regular Lagrangian L and use as the nonlinear connection that canonically induced by L, a framed f(3, -l)-structure P2 of corank 2 naturally appears on TM. This reduces to that found by us in [3] when L = F2 , for F the fundamental function of a Finsler space Fn = (M,F). Then we show that on some conditions for L the restriction of P2 to the submanifold L = 1 of TO M is an almost paracontact structure on this submanifold. The conditions taken on L hold for the -Lagrangians introduced by P.L.Antonelli and D. Hrimiuc in [2] as well as for L = F2.

5

Harmonic sections in the unitary tangent bundle

Oniciuc C.

Demonstratio Mathematica

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2001

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Vol. 34, nr 3

681-692

EN

The problems studied in this paper are connected with the harmonicity of the canonical projection TT : TM - M, as well as, with the harmonicity of the vector fields x(M) thought of as maps from M to TM. We have considered on TM a new Riemannian metric G.

6

Another Kaehler structure on the tangent bundle of a space form

Papaghiuc N.

Demonstratio Mathematica

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1998

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Vol. 31, nr 4

855-866

EN

It is obtained a Kaehler structure on the tangent bundle of an n-dimensional Riemannian manifold of constant positive sectional curvature. It is skown that this Kaehler structure is Ricci flat if n=2 but, generally, it is not a Kaehler Einstein structure.