TAILIEUCHUNG - Invariant structures and gauge transformation of almost contact metric manifolds

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 doi: 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: • Accepted/Published Online: • Final Version: 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 .

• Toán học
• Gauge transformation
• Cosymplectic manifold
• Almost contact 3 structure
• 3 Sasakian manifold
• 3 cosymplectic manifold
• Slant submanifold
• Transformation of Mass
• Relativistic Energy
• Relativistic Momentum
• The Maxwell Equations
• Gauge Transformations
• Moving Charge
• Mean curvature
• Sectional curvature
• K Ricci curvature
• Semi slant submanifold
• Bi slant submanifold
• Cosymplectic space form
• Semi slant
• Bi slant
• Almost contact 3 structure manifold
• Semi slant and bi slant submanifold
• 3 cosymplectic
• Sasakian manifold
• Point wise slant submanifold
• Almost contact geometry
• Almost contact 3 structure manifolds
• Warped product
• Semi slant submanifold
• Kenmotsu manifold
• Canonical structure
• Locally product manifold
• Hemi slant submanifold
• Slant distribution
• Riemannian manifold
• Parallel canonical structures
• Anti invariant
• Warped product submanifold
• Skew semi invariant submanifold
• Invariant distribution
• Chen’s invariant
• Squared mean curvature
• Quaternionic space form
• S manifolds
• Kaehler manifold
• Ricci tensor
• Curvature inequalities
• Scalar curvature