Vanishing theorems on (ℓ|k) -strong Kähler manifolds with torsion

S. Ivanov*, G. Papadopoulos

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)

Abstract

We derive sufficient conditions for the vanishing of plurigenera, p m (J) , m > 0, on compact (ℓ | k) -strong, ωℓ∧∂∂̄ωk=0, Kähler manifolds with torsion. In particular, we show that the plurigenera of closed (ℓ | k) -strong manifolds, k < n - 1, for which hol(∇;̂)⊆SU(n) vanish, where ∇;̂ is the Hermitian connection with skew-symmetric torsion. As a consequence all generalized k-Gauduchon manifolds for which hol(∇;̂)⊆SU(n) do not admit holomorphic (n, 0) forms. Furthermore we show that all conformally balanced, (ℓ | k) -strong Kähler manifolds with torsion, k ≠ n - 1, are Kähler. We also give several examples of (ℓ | k) -strong Kähler and Calabi-Yau manifolds with torsion. 

Original languageEnglish
Pages (from-to)147-164
Number of pages18
JournalADVANCES IN MATHEMATICS
Volume237
DOIs
Publication statusPublished - 1 Apr 2013

Keywords

  • Conformally balanced
  • Generalized k-Gauduchon manifolds
  • Kaehler manifolds with torsion
  • Vanishing of the plurigenera

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