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Invariant structures and gauge transformation of almost contact metric manifolds

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In this paper, conditions for K-contact, Sasakian, and cosymplectic structures to be invariant under gauge transformation are found. Moreover, the same question is studied for 3-Sasakian, 3-almost contact, and 3-cosymplectic manifolds. | Turk J Math (2016) 40: 1274 – 1282 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ doi:10.3906/mat-1406-72 Research Article Invariant structures and gauge transformation of almost contact metric manifolds Morteza MIRMOHAMMAD REZAII∗, Mehrnoosh ZANDI Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran Received: 30.06.2014 • Accepted/Published Online: 09.02.2016 • Final Version: 02.12.2016 Abstract: In this paper, conditions for K-contact, Sasakian, and cosymplectic structures to be invariant under gauge transformation are found. Moreover, the same question is studied for 3-Sasakian, 3-almost contact, and 3-cosymplectic manifolds. Finally, it is shown that a slant submanifold of an almost contact metric manifold is invariant by gauge transformation. Key words: Gauge transformation, cosymplectic manifold, almost contact 3-structure, 3-Sasakian manifold, 3-cosymplectic manifold, slant submanifold 1. Introduction Gauge transformation of a contact metric manifold was introduced by Tanno [12]. He obtained a contact metric structure invariant under gauge transformation. Sakamoto and Takemora introduced the gauge transformation of an almost contact metric manifold in [9]. The study of gauge transformation has been considered by several authors (see for instance [7, 8, 11]). In this paper, we find conditions in which k-contact structures, Sasakian structures, and cosymplectic structures are invariant under gauge transformation and we see that if the gauge transformation of a Sasakian manifold is k-contact then it is Sasakian. We study gauge transformation of 3-Sasakian structures, almost contact 3-structures, and 3-cosymplectic structures and take conditions in which these structures are invariant under gauge transformation. Finally, we study gauge transformation of slant submanifolds of almost contact structures. We see that these submanifolds are invariant under gauge .