Invariant structures and gauge transformation of almost contact metric manifolds
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. Finally, it is shown that a slant submanifold of an almost contact metric manifold is invariant by gauge transformation.
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- [1] Blair DE. Riemannian Geometry of Contact and Symplectic Manifolds. Boston, MA, USA: Brikhauser, 2002.
- [2] Falcitelli M, Ianus S, Pastore AM. Riemannian Submersions and Related Topics. Singapore: World Scientific, 2004.
- [3] G¨und¨uzalp Y, S¸ahin B. Paracontact semi-Riemannian submersions. Turk J Math 2013; 37: 114-128.
- [4] Gupta R Sh, Sharfuddin A. Slant lightlike submanifolds of indefinite Kenmotsu manifolds. Turk J Math 2011; 35: 115-127.
- [5] Kashiwada T. On a contact 3-structure. Math Z 2001; 238: 829-832.
- [6] Kuo YY. On almost contact 3-structure. Tohoku Math J 1970; 22: 325-332.
- [7] Matzeu P, Munteanu MI. Classification of almost contact structures associated with a strongly pseudo-convex CR-structure. Riv Mat Univ Prama 2000; 3: 127-142.
- [8] Munteanu MI. Harmonicity and gauge transformations in dimension 3. Geom J 2003; 77: 140-151.
- [9] Sakamoto K, Takemura Y. On almost contact structures belonging to a CR structure. Kodai Math J 1980; 3: 144-161.
- [10] Sular S, Ozg¨ur C. Contact CR-warped product submanifolds in generalized Sasakian space forms. Turk J Math ¨ 2012; 36: 485-497.
- [11] Tanno S. The bocher type curvarture tensor of contact Riemannian structure. Hokaido J Math 1990; 19: 55-66.
- [12] Tanno S. Variational problems on contact Riemannian manifolds. Trans Amer Math Soc 1989; 314: 349-379.
- [13] Udriste C. Structures presque coquaternioniennes Bull Math Soc Sci Math R S Roumanie 1969; 13: 487-507.