ANTI-INVARIANT RIEMANNIAN SUBMERSIONS FROM ALMOST PRODUCT RIEMANNIAN MANIFOLDS

Year 2013, Volume: 1 Issue: 1, 58 - 66, 01.06.2013

Yilmaz Gunduzalp

Abstract

In this paper, we introduce anti-invariant Riemannian submersions from almost product Riemannian manifolds onto Riemannian manifolds.We give an example, investigate the geometry of foliations which are arisenfrom the definition of a Riemannian submersion and check the harmonicity ofsuch submersions

Keywords

-

References

• Baird, P. and Wood, J.C., Harmonic morphisms between Riemannia manifolds. Oxford sci- ence publications, 2003.
• Bourguignon, J.P., Lawson, H.B., A mathematician’s visit to Kaluza- Klein theory. Rend. Sem. Mat. Univ. Politec. Torino, Special Issue (1989), 143-163.
• Bourguignon, J.P., Lawson, H.B., Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79(1981), 189-230.
• Eells, J., Sampson, J.H., Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86(1964), 109-160.
• Falcitelli, M., Ianus, S. and Pastore, A.M., Riemannian submersions and related topics. World Scientific, 2004.
• Gray, A., Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16(1967), 715-737.
• G¨und¨uzalp, Y., Slant submersions from almost product Riemannian manifolds. Turkish Jour- nal of Mathematics accepted, doi: 10.3906/mat-1205-64.
• Ianus, S., Mazzocco, R. and Vilcu, G. E, Riemannian submersions from quaternionic mani- folds. Acta Appl. Math. 104(2008), 83-89.
• Ianus, S. and Visinescu, M., Kaluza-Klein theory with scalar fields and generalised Hopf manifolds. Classical Quantum Gravity 4(1987), 1317-1325.
• Ianus, S. and Visinescu, M., Space-time compactification and Riemannian submersions. The mathematical heritage of C.F. Gauss, World Sci. Publ., River Edge, NJ, (1991),358-371.
• Mustafa, M.T., Applications of harmonic morphisms to gravity. J. Math. phys. 41(2000), 6918-6929.
• O’Neill, B., The fundamental equations of a submersion. Michigan Math. J. 13(1966), 459- 4
• Park, K.S., H-slant submersions. Bull. Korean Math. Soc. 49(2012), 329-338.
• S.ahin, B., Slant submersions from almost Hermitian manifolds. Bull. Math. Soc.Sci. Math. Roumanie Tome 54(102) (2011), 93-105.
• S.ahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds. Cent. Eur. J. Math. 8(3)(2010), 437-447.
• Watson, B., Almost Hermitian submersions. J. Diff. Geom. 11(1976) 147-165.
• Watson, B., G,G’-Riemannian submersions and nonlinear gauge field equations of general relativity. Global analysis on manifolds Teubner-Texte Math.,57,Teubner, Leipzig, (1983), 324-2
• Yano, K. and Kon, M., Structures on manifolds. World Scientific. 1984.
• Department of Mathematics, Dicle University, 21280, Diyarbakır-Turkey
• E-mail address: [e-mail]