Rotational Self-Shrinkers in Euclidean Spaces

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ARSLAN K., Aydın Y., Sokur B.

International Electronic Journal of Geometry, cilt.17, sa.1, ss.34-43, 2024 (ESCI) identifier

  • 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
  • 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.