Abstract
We introduce anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions. We also find necessary and sufficient conditions for a Langrangian Riemannian submersion, a special anti-invariant Riemannian submersion, to be totally geodesic. Moreover, we obtain decomposition theorems for the total manifold of such submersions.
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References
Altafini C., Redundant robotic chains on Riemannian submersions IEEE Transactions on Robotics and Automation, 2004, 20(2), 335–340
Baird P., Wood J.C., Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press, Oxford, 2003
Chinea D., Almost contact metric submersions, Rend. Circ. Mat. Palermo, 1985, 34(1),89–104
Eells J., Sampson J.H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 1964, 86, 109–160
Escobales R.H. Jr., Riemannian submersions from complex projective space, J. Differential Geom., 1978, 13(1), 93–107
Falcitelli M., Ianus S., Pastore A.M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004
Gray A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 1967, 16, 715–737
Ianus S., Mazzocco R., Vilcu G.E., Riemannian submersions from quaternionic manifolds, Acta Appl. Math., 2008, 104(1), 83–89
Marrero J.C., Rocha J., Locally conformal Khler submersions, Geom. Dedicata, 1994, 52(3), 271–289
O’Neill B., The fundamental equations of a submersion, Mich. Math. J., 1966, 13, 458–469
Ponge R., Reckziegel H., Twisted products in pseudo-Riemannian geometry, Geom. Dedicata, 1993, 48(1), 15–25
Watson B., Almost Hermitian submersions, J. Differential Geometry, 1976, 11(1), 147–165
Yano K., Kon M., Structures on Manifolds, World Scientific, Singapore, 1984
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Ṣahin, B. Anti-invariant Riemannian submersions from almost Hermitian manifolds. centr.eur.j.math. 8, 437–447 (2010). https://doi.org/10.2478/s11533-010-0023-6
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DOI: https://doi.org/10.2478/s11533-010-0023-6