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arXiv · 1202.6470

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

Stefan Ivanov·George Papadopoulos
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Abstract

We derive sufficient conditions for the vanishing of plurigenera, $p_m(J), m>0$, on compact (l|k)-strong, $ω^l\wedge \partial\bar\partial ω^k=0$, Kaehler manifolds with torsion. In particular, we show that the plurigenera of compact (l|k)-strong manifolds, k<n-1, for which the holonomy of the unique Hermitian connection with skew-symmetric torsion is contained in SU(n) vanish. As a consequence all generalized k-Gauduchon manifolds with holonomy of the Hermitian connection with skew-symmetric torsion contained in SU(n) do not admit holomorphic (n,0) forms. Furthermore we show that all conformally balanced, (l|k)-strong Kaehler manifolds with torsion, k<n-1, are Kähler. We also give several compact examples of (l|k)-strong Kaehler and Calabi-Yau manifolds with torsion.

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Stefan Ivanov, George Papadopoulos. 2012-02-29. Vanishing theorems on (l|k)-strong Kaehler manifolds with torsion. https://arxiv.org/abs/1202.6470

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