Invariant submanifolds in golden Riemannian manifolds

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Atıf İçin Kopyala

Gök M., Keleş S., Kılıç E.

Communications Faculty Of Science University of Ankara Series A1 Mathematics and Statistics, cilt.69, sa.2, ss.125-138, 2020 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 69 Sayı: 2
• Basım Tarihi: 2020
• Doi Numarası: 10.31801/cfsuasmas.635434
• Dergi Adı: Communications Faculty Of Science University of Ankara Series A1 Mathematics and Statistics
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.125-138
• Anahtar Kelimeler: Golden structure, golden Riemannian manifold, invariant submanifold
• Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

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 sub-manifold 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 sub-manifold 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.