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

S. Ivanov; G. Papadopoulos

doi:10.1016/j.aim.2012.12.019

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

S. Ivanov^*, G. Papadopoulos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

29 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 language	English
Pages (from-to)	147-164
Number of pages	18
Journal	ADVANCES IN MATHEMATICS
Volume	237
DOIs	https://doi.org/10.1016/j.aim.2012.12.019
Publication status	Published - 1 Apr 2013

Keywords

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

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10.1016/j.aim.2012.12.019

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title = "Vanishing theorems on (ℓ|k) -strong K{\"a}hler manifolds with torsion",

abstract = "We derive sufficient conditions for the vanishing of plurigenera, p m (J) , m > 0, on compact (ℓ | k) -strong, ωℓ∧∂{\=∂}ωk=0, K{\"a}hler 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 K{\"a}hler manifolds with torsion, k ≠ n - 1, are K{\"a}hler. We also give several examples of (ℓ | k) -strong K{\"a}hler and Calabi-Yau manifolds with torsion. ",

keywords = "Conformally balanced, Generalized k-Gauduchon manifolds, Kaehler manifolds with torsion, Vanishing of the plurigenera",

author = "S. Ivanov and G. Papadopoulos",

note = "{\textcopyright} 2013 Elsevier Ltd.",

year = "2013",

month = apr,

day = "1",

doi = "10.1016/j.aim.2012.12.019",

language = "English",

volume = "237",

pages = "147--164",

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TY - JOUR

T1 - Vanishing theorems on (ℓ|k) -strong Kähler manifolds with torsion

AU - Ivanov, S.

AU - Papadopoulos, G.

PY - 2013/4/1

Y1 - 2013/4/1

N2 - 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.

AB - 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.

KW - Conformally balanced

KW - Generalized k-Gauduchon manifolds

KW - Kaehler manifolds with torsion

KW - Vanishing of the plurigenera

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DO - 10.1016/j.aim.2012.12.019

M3 - Article

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SN - 0001-8708

VL - 237

SP - 147

EP - 164

JO - ADVANCES IN MATHEMATICS

JF - ADVANCES IN MATHEMATICS

ER -

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

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Keywords

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