Aydin Gezer and Arif A. Salimov July 2008 The Arabian Journal for Science and Engineering, Volume 33, Number 2A 283 ALMOST COMPLEX STRUCTURES ON THE TENSOR BUNDLES * Aydin Gezer † and Arif A. Salimov Department of Mathematics, Faculty of Arts and Sciences, Ataturk University, 25240, Erzurum, Turkey اﻟﺨﻼﺻـﺔ: ﺎرΒΘϋ اϦﻜϤϳ أ نM ﺼﻒϟ ﺔϴϠοﻔﺎΗ ΐϴﺮاآΗ ﻜﻮنΗ C ∞ ﺎѧﻬϟ ﻮرδѧϨΘϟ اﺔϣﺰΣ و( ) p q T M ﻮعѧϧ Ϧѧϣ ( ,) p q . وﻮعϧ Ϧϣ ﻮرδϨΘϟ اﺔϣﺰΣ أنﺮوفόϤϟ اϦϣ (1, ) q ـϟ M ΒϴﺮآΗ  ﺎΒϳﻘﺮΗ ϞﻜθΗ  ﺎﻘﺪόϣ  اΖϧ آﺎ إذا،ϲοﺮϋ ϊﻘﻄϣ ﻰϠϋ M ѧΒϴﺮآΗ  ﺎѧΒϳﻘﺮΗ ϞﻜθѧΗ  ﺎﺪѧﻘόϣ  ا. وﺬاѧ هﺪفѧﻬϳ ϴΒѧη ﺔϠπѧόϣ ﺔѧγ دراﻰѧϟ إΚѧΤΒϟ ا ﻬﺔΑ ﻮرδѧϨΗ ﺔѧϣﺰΤ ( ) p q T M ﻮعѧϧ ( ,) p q و1 p > . ﻮفѧѧѧγ وΐѧѧѧϴﺮاآΗ أنϦ ﺮهѧѧѧΒϧ M ѧѧѧΒϴﺮآΗ  ﺎѧѧѧΒϳﻘﺮΗ ϞﻜθѧѧѧΗ  ﺎ ﺪѧѧѧﻘόϣ  اϕ ﻚϟ ﺬѧѧѧ وآ( ) p q T M و 1 p > ΚϴΣ ϲοﺮϋ ϊﻘﻄϣ ﻰϠϋ ϕ ϴϠϣﻜﺎΗ ﺔ. وﺔϨﺮهΒϟ اﺪϤΘόΗ ) ﺎتΒΛ اﻹ( ﺔϴϠοﻔﺎΘϟ اϢϴϣﺎόΘϟ اξόΑ ﻰϠϋ . * This paper is supported by The Scientific & Technological Council of Turkey (TUBITAK). To whom correspondence should be addressed † E-mail: agezer@atauni.edu.tr ; gezeraydin@hotmail.com Paper Received 27 September 2006; Revised 24 December 2007; Accepted 20 February 2008