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J. Korean Math. Soc. 2008; 45(2): 367-376

Printed March 1, 2008

Copyright © The Korean Mathematical Society.

Diagonal lifts of tensor fields of type $(1,1)$ on cross-sections in tensor bundles and its applications

Aydin Gezer and Arif Salimov

Ataturk University, Ataturk University

Abstract

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The main purpose of this paper is to investigate diagonal lift of tensor fields of type $(1,1)$ from manifold to its tensor bundle of type $(p,q)$ and to prove that when a manifold $M_{n}$ admits a K\"{a}hlerian structure $(\varphi ,g)$, its tensor bundle of type $(p,q)$ admits an complex structure.

Keywords: tensor bundle, diagonal lift, complex structure, Nijenhuis tensor, Kahlerian structure

MSC numbers: 53C07, 53B05, 55R10, 53C55

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