Abstract
We introduce anti-invariant ξ⊥ -Riemannian submersions from almostcontact 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 suchsubmersions. We also find necessary and sufficient conditions for a special anti-invariant ξ⊥ -Riemannian submersion to be totally geodesic.Moreover, we obtain decomposition theorems for the total manifold ofsuch submersions.
Keywords
Riemannian submersion Sasakian manifold Anti-invariant ξ⊥ -Riemannainsubmersion2000 AMS Classification:53C25 53C40 53C50
References
- Altafini, C. Redundant robotic chains on Riemannian submersions, IEEE Transactions on Robotics and Automation, 20(2), 335-340, 2004.
- Blair, D. E. Contact manifold in Riemannian geometry,(Lecture Notes in Math., 509, Springer-Verlag, Berlin-New York, 1976).
- Baird, P., Wood, J. C. Harmonic Morphisms Between Riemannian Manifolds, (London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press, Oxford, 2003).
- Chinea, C. Almost contact metric submersions, Rend. Circ. Mat. Palermo, 43(1), 89–104, 198 Eells, J., Sampson, J. H. Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86, 109–160, 1964.
- 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 submersion, J. Math. Mech., 16, 715–737, 1967.
- Ianus, S., Pastore A. M. Harmonic maps on contact metric manifolds, Ann. Math. Blaise Pascal, 2(2), 43–53, 1995.
- O’Neill, B. The fundamental equations of a submersion, Mich. Math. J.,13, 458–469, 1966. Ponge, R. Reckziegel, H. Twisted products in pseudo-Riemannian geometry, Geom. Dedicata, 48(1), 15–25, 1993.
- Sahin, B. Anti-invariant Riemannian submersions from almost hermitian manifolds, Cent. Eur. J. Math., 8(3), 437–447, 2010.
- Sasaki, S., Hatakeyama, Y. On differentiable manifolds with contact metric structure, J. Math. Soc. Japan, 14, 249–271, 1961.
- Watson, B. Almost Hermitian submersions, J. Differential Geometry, 11(1), 147–165, 1976.
Abstract
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Keywords
References
- Altafini, C. Redundant robotic chains on Riemannian submersions, IEEE Transactions on Robotics and Automation, 20(2), 335-340, 2004.
- Blair, D. E. Contact manifold in Riemannian geometry,(Lecture Notes in Math., 509, Springer-Verlag, Berlin-New York, 1976).
- Baird, P., Wood, J. C. Harmonic Morphisms Between Riemannian Manifolds, (London Mathematical Society Monographs, 29, Oxford University Press, The Clarendon Press, Oxford, 2003).
- Chinea, C. Almost contact metric submersions, Rend. Circ. Mat. Palermo, 43(1), 89–104, 198 Eells, J., Sampson, J. H. Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86, 109–160, 1964.
- 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 submersion, J. Math. Mech., 16, 715–737, 1967.
- Ianus, S., Pastore A. M. Harmonic maps on contact metric manifolds, Ann. Math. Blaise Pascal, 2(2), 43–53, 1995.
- O’Neill, B. The fundamental equations of a submersion, Mich. Math. J.,13, 458–469, 1966. Ponge, R. Reckziegel, H. Twisted products in pseudo-Riemannian geometry, Geom. Dedicata, 48(1), 15–25, 1993.
- Sahin, B. Anti-invariant Riemannian submersions from almost hermitian manifolds, Cent. Eur. J. Math., 8(3), 437–447, 2010.
- Sasaki, S., Hatakeyama, Y. On differentiable manifolds with contact metric structure, J. Math. Soc. Japan, 14, 249–271, 1961.
- Watson, B. Almost Hermitian submersions, J. Differential Geometry, 11(1), 147–165, 1976.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Mathematics |
| Authors | |
| Publication Date | March 1, 2013 |
| Published in Issue | Year 2013 Volume: 42 Issue: 3 |