ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53 Salimov A. A and Mağden A, Atatürk University, Turkey Problems of lifts of affinor structures on a pure-cross section. Section: 2 1991 MS Classification: 53 Salimov Arif A and Mağden Abdullah, Atatürk University, Erzurum Turkey: Problems of lifts of affinor structures on a pure-cross section. Let M_{n} be an n-dimensional differentiable manifold of class C^{∞}, T_{0}^{q}(M_{n}), q > 0 its tensor bundle andφ ∈ T_{1}^{1}(M_{n})be affinor structure onM_{n}and ξ ∈ T_{0}^{q}(M_{n})the pure tensor field with respect to theφ-structure. The main purpose of the present paper is to study the behaviour on the pure cross-section of the lifts of theφ-structure. We have founded the complete lift^{c}φhas alongξ(M_{n})components

cφ_{k}^{i} = φ_{k}^{i}, ^{c}φi ; k̄ = 0, ^{c}φī ; k = −(Φ_{varphi}ξ)_{lk_{1}···k_{q}}, ^{c}φī ; k̄ = φ_{i_{1}}^{k_{1}}δ_{i_{2}}^{k_{2}} ⋯ δ_{i_{q}}^{k_{q}} (1).

with respect to the adapted(B, C)frame of the pure cross-section ξ(M_{n})(with respetc to the natural frame see [1]), whereΦ is the Tachibana operator. horizontal lift ^{H}φ [2]. Reference: [1] A. A. Salimov, The generalized Yano-Ako operator and complete lift of the tensor fields. Tensor (N. S)55 (1994), 142–146.

[2] A. A. Salimov, A new method in theory of lifts tensor fields to the tensor bundle, IZV. Vuz., Mathematics, 3 (1994), 69–75.