The Bochner technique and modification of the Ricci tensor

Limoncu M.

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, cilt.36, sa.3, ss.285-291, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 3
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s10455-009-9163-y
  • Dergi Adı: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.285-291
  • Anahtar Kelimeler: Bochner technique, Modification of the Ricci tensor, Vanishing theorems, Eigenvalue estimate
  • Anadolu Üniversitesi Adresli: Evet

Özet

In the well-known vanishing theorems of Bochner, the assumptions Ric a parts per thousand yen 0 and Ric a parts per thousand currency sign 0 are modified by using Hessian and Laplacian of a smooth positive function such that, when this function is constant, these assumptions return to Ric a parts per thousand yen 0 and Ric a parts per thousand currency sign 0. We prove that the assertions and results of Bochner's vanishing theorems still hold under these modified assumptions. Additionally, the assumption Ric a parts per thousand yen H > 0 given in the eigenvalue estimate theorem of Lichnerowicz is also modified in the same way, and we obtain estimates for the first positive eigenvalue of the Laplace operator.