Geodesic
H-anti-invariant submersions from almost quaternionic Hermitian manifolds
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 557-578
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As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples of such maps. Finally, we obtain some types of decomposition theorems.
As a generalization of anti-invariant Riemannian submersions and Lagrangian Riemannian submersions, we introduce the notions of h-anti-invariant submersions and h-Lagrangian submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate some properties: the integrability of distributions, the geometry of foliations, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic and give some examples of such maps. Finally, we obtain some types of decomposition theorems.
DOI : 10.21136/CMJ.2017.0143-16
Classification : 53C15, 53C26
Keywords: Riemannian submersion; Lagrangian Riemannian submersion; decomposition theorem; totally geodesic 
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Park, Kwang-Soon. H-anti-invariant submersions from almost quaternionic Hermitian manifolds. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 557-578. doi: 10.21136/CMJ.2017.0143-16

[1] Altafini, C.: Redundant robotic chains on Riemannian submersions. IEEE Transactions on Robotics and Automation 20 (2004), 335-340. | DOI

[2] Alekseevsky, D. V., Marchiafava, S.: Almost complex submanifolds of quaternionic manifolds. Steps in differential geometry Kozma, L. et al. Proc. of the colloquium on differential geometry, Debrecen, 2000, Inst. Math. Inform. Debrecen (2001), 23-38. | MR | JFM

[3] Baird, P., Wood, J. C.: Harmonic Morphisms between Riemannian Manifolds. London Mathematical Society Monographs, New Series 29, Oxford University Press, Oxford (2003). | DOI | MR | JFM

[4] Besse, A. L.: Einstein Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, Berlin (1987). | DOI | MR | JFM

[5] Bourguignon, J.-P.: A mathematician's visit to Kaluza-Klein theory. Conf. on Partial Differential Equations and Geometry, Torino, 1988, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (1989), 143-163. | MR | JFM

[6] Bourguignon, J. P., Jr., H. B. Lawson: Stability and isolation phenomena for Yang-Mills fields. Commum. Math. Phys. 79 (1981), 189-230. | DOI | MR | JFM

[7] Chinea, D.: Almost contact metric submersions. Rend. Circ. Mat. Palermo II. Ser. 34 (1985), 89-104. | DOI | MR | JFM

[8] Cortés, V., Mayer, C., Mohaupt, T., Saueressig, F.: Special geometry of Euclidean supersymmetry I. Vector multiplets. J. High Energy Phys. (electronic) 3 (2004), no. 028, 73 pages. | DOI | MR

[9] Falcitelli, M., Ianus, S., Pastore, A. M.: Riemannian Submersions and Related Topics. World Scientific Publishing, River Edge (2004). | DOI | MR | JFM

[10] Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16 (1967), 715-737. | MR | JFM

[11] Ianuş, S., Mazzocco, R., lcu, G. E. Vî: Riemannian submersions from quaternionic manifolds. Acta. Appl. Math. 104 (2008), 83-89. | DOI | MR | JFM

[12] Ianus, S., Vişinescu, M.: Kaluza-Klein theory with scalar fields and generalised Hopf manifolds. Classical Quantum Gravity 4 (1987), 1317-1325. | DOI | MR | JFM

[13] Ianus, S., Visinescu, M.: Space-time compactification and Riemannian submersions. The Mathematical Heritage of C. F. Gauss, Collect. Pap. Mem. C. F. Gauss, World Sci. Publ., River Edge (1991), 358-371. | DOI | MR | JFM

[14] Marrero, J. C., Rocha, J.: Locally conformal Kähler submersions. Geom. Dedicata 52 (1994), 271-289. | DOI | MR | JFM

[15] Mémoli, F., Sapiro, G., Thompson, P.: Implicit brain imaging. NeuroImage 23 (2004), 179-188. | DOI

[16] Mustafa, M. T.: Applications of harmonic morphisms to gravity. J. Math. Phys. 41 (2000), 6918-6929. | DOI | MR | JFM

[17] O'Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 13 (1966), 458-469. | DOI | MR | JFM

[18] Park, K.-S.: H-semi-invariant submersions. Taiwanese J. Math. 16 (2012), 1865-1878. | DOI | MR | JFM

[19] Park, K.-S.: H-slant submersions. Bull. Korean Math. Soc. 49 (2012), 329-338. | DOI | MR | JFM

[20] Park, K.-S.: H-semi-slant submersions from almost quaternionic Hermitian manifolds. Taiwanese J. Math. 18 (2014), 1909-1926. | DOI | MR | JFM

[21] Ponge, R., Reckziegel, H.: Twisted products in pseudo-Riemannian geometry. Geom. Dedicata 48 (1993), 15-25. | DOI | MR | JFM

[22] Sahin, B. \d: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Cent. Eur. J. Math. 8 (2010), 437-447. | DOI | MR | JFM

[23] Şahin, B.: Riemannian submersions from almost Hermitian manifolds. Taiwanese J. Math. 17 (2013), 629-659. | DOI | MR | JFM

[24] Watson, B.: Almost Hermitian submersions. J. Differ. Geom. 11 (1976), 147-165. | DOI | MR | JFM

[25] Watson, B.: $G,G'$-Riemannian submersions and non-linear gauge field equations of general relativity. Global Analysis -- Analysis on Manifolds Teubner-Texte Math. 57, Teubner, Leipzig (1983), 324-349. | MR | JFM

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