Invariant submanifolds in golden Riemannian manifolds

Yıl 2020, Cilt: 69 Sayı: 2, 1119 - 1132, 31.12.2020

Erol Kılıç , Mustafa Gök , Sadık Keleş

https://doi.org/10.31801/cfsuasmas.635434

Cited By: 4

Öz

In this paper, we study invariant submanifolds of a golden Riemannian manifold with the aid of induced structures on them by the golden structure of the ambient manifold. We demonstrate that any invariant submanifold in a locally decomposable golden Riemannian manifold leaves invariant the locally decomposability of the ambient manifold. We give a necessary and sufficient condition for any submanifold in a golden Riemannian manifold to be invariant. We obtain some necessary conditions for the totally geodesicity of invariant submanifolds. Moreover, we find some facts on invariant submanifolds. Finally, we present an example of an invariant submanifold.

Anahtar Kelimeler

Invariant Submanifold, Golden Structure, Golden Riemannian Manifold

Kaynakça

• Shaw, S., Pierre, C., Non-linear normal modes and invariant manifolds, J. Sound Vib., 150(1) (1991), 170-173.
• Gorban, A. N., Karlin, I. V., Method of invariant manifold for chemical kinetics, Chem. Eng. Sci., 58(21) (2003), 4751-4768.
• Yano, K., Ishihara, S., Invariant submanifolds of an almost contact manifold, Kodai Math. Sem. Rep., 21(3) (1969), 350-364.
• Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(2) (1972), 93-103.
• Kon, M., Invariant submanifolds of normal contact metric manifolds, Kodai Math. Sem. Rep., 25(3) (1973), 330-336.
• Kon, M., Invariant submanifolds in Sasakian manifolds, Math. Ann., 219(3) (1976), 277-290.
• Adati, T., Submanifolds of an almost product Riemannian manifold, Kodai Math. J., 4(2) (1981), 327-343.
• Takemura, Y., On the invariant submanifold of a CR-manifold, Kodai Math. J., 5(3) (1982), 416-425.
• Crâşmăreanu, M. C., Hreţcanu, C. E., Golden differential geometry, Chaos Solitons Fractals, 38(5) (2008), 1229-1238.
• Etayo, F., Santamaría, R., Upadhyay, A., On the geometry of almost golden Riemannian manifolds, Mediterr. J. Math., 14(5) (2017), Article ID 187, 14 pages.
• Gök, M., Keleş, S., Kılıç, E., Schouten and Vrănceanu connections on golden manifolds, Int. Electron. J. Geom. 12(2) (2019), 169-181.
• Erdoğan, F. E., Yıldırım, C., On a study of the totally umbilical semi-invariant submanifolds of golden Riemannian manifolds, J. Polytechnic, 21(4) (2018), 967-970.
• Blaga, A. M., Hreţcanu, C. E., Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold, Novi Sad J. Math., 48(2) (2018), 55-80.
• Hreţcanu, C. E., Blaga, A. M., Slant and semi-slant submanifolds in metallic Riemannian manifolds, J. Funct. Spaces, 2018 (2018), Article ID 2864263, 13 pages.
• Hreţcanu, C. E., Blaga, A. M., Hemi-slant submanifolds in metallic Riemannian manifolds, Carpathian J. Math., 35(1) (2019), 59-68.
• Gök, M., Keleş, S., Kılıç, E., Some characterizations of semi-invariant submanifolds of golden Riemannian manifolds, Mathematics, 7(12) (2019), Article ID 1209, 12 pages.
• Hreţcanu, C. E., Crâşmăreanu, M. C., On some invariant submanifolds in a Riemannian manifold with golden structure, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat., (N.S.) 53(suppl. 1) (2007), 199-211.
• Hreţcanu, C. E., Crâşmăreanu, M. C., Applications of the golden ratio on Riemannian manifolds, Turk. J. Math., 33(2) (2009), 179-191.
• Goldberg, S. I., Yano, K., Polynomial structures on manifolds, Kodai Math. Sem. Rep., 22(2) (1970), 199-218.
• Yano, K., Kon, M., Structures on Manifolds, World Scientific, Singapore, 1984.