Prolongations of Hypersurfaces to Vector Bundles

Year 2017, Volume: 7, 73 - 82, 19.12.2017

Mustafa Özkan , Erdoğan Esin

Abstract

This paper introduces and studies the concept of prolongations of a hypersurface to a vector bundle. We develop the theory of hypersurfaces using the metric tensor which is the complete lift of the metric tensor of the initial manifold.

Keywords

Prolongation, vector bundle, hypersurface

References

• Gancarzewicz, J., Rahmani, N., Horizontal lift of linear connections to vector bundles associated with the principal bundle of linear frames, Colloquia Mathematics Societatis Janos Bolyai, 56(1989), 273--284.
• Leon, M.D., Rodrigues, P.R., Methods of Differential Geometry in Analytical Mechanics, North-Holland Mathematics Studies 158, Nort-Holland, 1989.
• Omran, T., Sharffuddin, A., Husain, S.I., Lifts of structures on manifolds, Publications De L'institut Math. J., 36(50)(1984), 93--97.
• Özkan, M., Esin, E., Vertical lifts of tensor fields to vector bundle, Algebras Groups Geom., 25(1)(2008), 21--30.
• Özkan, M., Complete lifts of tensor fields to vector bundle, Int. J. Math. Sci. App., 1(2)(2012), 593--599.
• Özkan, M., Complete lifts of structures on manifold to vector subbundle, GUJS, 25(3)(2012), 661--664.
• Özkan, M., Keçilioğlu, O., Complete lift of a structure satisfying $F^{3}+F=0$ to vector subbundle, Hadronic J., 38(3)(2015), 295--305.
• Özkan, M., Prolongations of golden structures to tangent bundles, Differential Geometry-Dynamical Systems, 16(2014), 227--238.
• Özkan, M., Çıtlak, A.A., Taylan, E., Prolongations of golden structure to tangent bundle of Order $2$, GUJS, 28(2)(2015), 253--258.
• Özkan, M., Yılmaz, F., Prolongations of golden structures to tangent bundles of order $r$. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, 65(1)(2016), 35--47.
• Özkan, M., Taylan, E., Çıtlak, A. A., On lifts of silver structure, Journal of Science and Arts, 2(39)(2017), 223--234.
• Poor, W.A., Differential Geometric Structures, McGraw-Hill, New York, 1981.
• Saunders, D.J., The Geometry of Jet Bundles, Cambridge University Press, Cambridge, 1989.
• Tani, M., Prolongations of hypersurfaces to tangent bundles, Kodai Math. Semp. Rep., 21(1969), 85--96.
• Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.
• Yıldırım, M., Esin, E., Vertical and complete lifts to vector bundle, Algebras Groups Geom., 24(1)(2007), 75--84.