Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 69 Sayı: 2, 1119 - 1132, 31.12.2020
https://doi.org/10.31801/cfsuasmas.635434

Öz

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.

Invariant submanifolds in golden Riemannian manifolds

Yıl 2020, Cilt: 69 Sayı: 2, 1119 - 1132, 31.12.2020
https://doi.org/10.31801/cfsuasmas.635434

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.

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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Erol Kılıç 0000-0001-7536-0404

Mustafa Gök 0000-0001-6346-0758

Sadık Keleş 0000-0003-3981-2092

Yayımlanma Tarihi 31 Aralık 2020
Gönderilme Tarihi 22 Ekim 2019
Kabul Tarihi 9 Mayıs 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 2

Kaynak Göster

APA Kılıç, E., Gök, M., & Keleş, S. (2020). Invariant submanifolds in golden Riemannian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1119-1132. https://doi.org/10.31801/cfsuasmas.635434
AMA Kılıç E, Gök M, Keleş S. Invariant submanifolds in golden Riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2020;69(2):1119-1132. doi:10.31801/cfsuasmas.635434
Chicago Kılıç, Erol, Mustafa Gök, ve Sadık Keleş. “Invariant Submanifolds in Golden Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 2 (Aralık 2020): 1119-32. https://doi.org/10.31801/cfsuasmas.635434.
EndNote Kılıç E, Gök M, Keleş S (01 Aralık 2020) Invariant submanifolds in golden Riemannian manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1119–1132.
IEEE E. Kılıç, M. Gök, ve S. Keleş, “Invariant submanifolds in golden Riemannian manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 2, ss. 1119–1132, 2020, doi: 10.31801/cfsuasmas.635434.
ISNAD Kılıç, Erol vd. “Invariant Submanifolds in Golden Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (Aralık 2020), 1119-1132. https://doi.org/10.31801/cfsuasmas.635434.
JAMA Kılıç E, Gök M, Keleş S. Invariant submanifolds in golden Riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1119–1132.
MLA Kılıç, Erol vd. “Invariant Submanifolds in Golden Riemannian Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 2, 2020, ss. 1119-32, doi:10.31801/cfsuasmas.635434.
Vancouver Kılıç E, Gök M, Keleş S. Invariant submanifolds in golden Riemannian manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1119-32.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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