Rotational Self-Shrinkers in Euclidean Spaces
International Electronic Journal of Geometry, cilt.17, sa.1, ss.34-43, 2024 (ESCI, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 17 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.36890/iejg.1330887
- Dergi Adı: International Electronic Journal of Geometry
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.34-43
- Anahtar Kelimeler: homothetic soliton, mean curvature flow, Rotational submanifold, self-shrinkers
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
The rotational embedded submanifolds of En+d were first studied by N. Kuiper. The special examples of this type are generalized Beltrami submanifolds and toroidals submanifold. The second author and et. all recently have considered 3−dimensional rotational embedded submanifolds in E5. They gave some basic curvature properties of this type of submaifolds. Self-similar flows emerge as a special solution to the mean curvature flow that preserves the shape of the evolving submanifold. In this article we consider self-similar submanifolds in Euclidean spaces. We obtained some results related with self-shrinking rotational submanifolds in Euclidean 5−space E5. Moreover, we give the necessary and sufficient conditions for these type of submanifolds to be homothetic solitons for their mean curvature flows.