The Morse Index for Manifolds with Constant Sectional Curvature

ŞİRİKÇİ N. İ.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.21, sa.4, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s00009-024-02682-5
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We compute the Morse index of a critical submanifold of the energy functional on the loop space of a manifold with constant sectional curvature. The case of constant non-positive sectional curvature is a known result and the case of a sphere has been proved by Klingenberg. We adapt Klingenberg's proof of the case of a sphere to the case of constant sectional curvature, to obtain the possible Morse indices of critical submanifolds of the energy functional.