Eigenvalue Estimates in Terms of the Extrinsic Curvature

Eker S., Değirmenci N.

Iranian Journal of Science and Technology, Transaction A: Science, cilt.45, sa.4, ss.1411-1416, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s40995-021-01136-x
  • Dergi Adı: Iranian Journal of Science and Technology, Transaction A: Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), BIOSIS, CAB Abstracts, Communication Abstracts, zbMATH
  • Sayfa Sayıları: ss.1411-1416
  • Anahtar Kelimeler: Dirac operator, Estimation of eigenvalues, Spin and Spinc geometry
  • Marmara Üniversitesi Adresli: Hayır

Özet

In this paper, we give a new lower bound for the eigenvalues of the Dirac operator defined on the Spin Riemannian hypersurface manifold endowed with 2-tensor, in terms of the Energy-Momentum tensor, scalar curvature and extrinsic curvature. Then this estimate is improved in two different ways by considering the conformal invariance of the Dirac operator. The first is given in term of the first eigenvalue of the Yamabe operator. The latter, is given in terms of the the area of a topological 2-sphere.