Slant submersions from almost product Riemannian manifolds

In this paper, we define the concept of almost product Riemannian submersion between almost product Riemannian manifolds. We introduce slant submersions from almost product Riemannian manifolds onto Riemannian manifolds. We give examples and investigate the geometry of foliations that arise from the definition of a Riemannian submersion. We also find necessary and sufficient conditions for a slant submersion to be totally geodesic.

Anahtar Kelimeler:

Riemannian submersion, almost product Riemannian submersion, almost product Riemannian manifold, slant submersion

Slant submersions from almost product Riemannian manifolds

Keywords:

Riemannian submersion, almost product Riemannian submersion, almost product Riemannian manifold, slant submersion,

PDF

___

At¸ ceken, M.: Slant submanifolds of a Riemannian product manifold. Acta Math. Sci. 30, 215–224 (2010).
Baird, P., Wood, J.C.: Harmonic Morphisms between Riemannian Manifolds. Oxford. Oxford Science Publications (2003).
Bourguignon, J.P., Lawson, H.B.: A mathematician’s visit to Kaluza-Klein theory. Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, 143–163 (1989).
Bourguignon, J.P., Lawson, H.B.: Stability and isolation phenomena for Yang-Mills fields. Comm. Math. Phys. 79, 189–230 (1981).
Chen, B.Y.: Geometry of Slant Submanifolds. Leuven. Katholieke Universiteit Leuven (1990).
Chen, B.Y.: Slant immersions. Bull. Austral. Math. Soc. 41(1), 135–147 (1990).
Falcitelli, M., Ianus, S., Pastore, A.M.: Riemannian Submersions and Related Topics. Singapore. World Scientific (2004).
Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16, 715–737 (1967). G¨ und¨ uzalp, Y.: C . arpım submersiyonlarının geometrisi uzerine (Turkish), PhD thesis, ˙In¨ on¨ u University, Malatya, Turkey (2011).
Ianus, S., Mazzocco, R., Vilcu, G.E: Riemannian submersions from quaternionic manifolds. Acta Appl. Math. 104, 83–89 (2008).
Ianus, S., Visinescu, M.: Kaluza-Klein theory with scalar fields and generalised Hopf manifolds. Classical Quantum Gravity 4, 1317–1325 (1987).
Ianus, S., Visinescu, M.: Space-time compactification and Riemannian submersions. The Mathematical Heritage of C.F. Gauss, 358371. River Edge, NJ, USA. World Scientific Publishing (1991).
Mustafa, M.T.: Applications of harmonic morphisms to gravity. J. Math. Phys. 41, 6918–6929 (2000).
O’Neill, B.: The fundamental equations of a submersion. Michigan Math. J. 13, 459–469 (1996).
Park, K.S.: H-slant submersions. Bull. Korean Math. Soc. 49, 329–338 (2012).
S ¸ahin, B.: Slant submersions from almost Hermitian manifolds. Bull. Math. Soc. Sci. Math. Roumanie Tome 54(102), 93–105 (2011).
S ¸ahin, B.: Slant submanifolds of an almost product Riemannian manifold. J. Korean Math. Soc. 43(4), 717–732 (2006).
Watson, B.: Almost Hermitian submersions. J. Diff. Geom. 11, 147–165 (1976).
Watson, B.: G,G’-Riemannian submersions and nonlinear gauge field equations of general relativity. Global Analysis on Manifolds. Teubner-Texte Math.. 57, 324–249 (1983).
Yano, Y., Kon, M.: Structures on manifolds. Singapore. World Scientific (1984).